Podcast
Questions and Answers
If 17 is added to twice a number, the result is 101. What is the number?
If 17 is added to twice a number, the result is 101. What is the number?
- 59
- 42 (correct)
- 84
- 118
The sum of two numbers is 156. If one number is three times the other, what are the two numbers?
The sum of two numbers is 156. If one number is three times the other, what are the two numbers?
- 15 and 141
- 39 and 117 (correct)
- 52 and 104
- 26 and 130
The sum of two numbers is 90, and their difference is 18. What are the two numbers?
The sum of two numbers is 90, and their difference is 18. What are the two numbers?
- 54 and 36 (correct)
- 56 and 34
- 52 and 38
- 58 and 32
Find three consecutive numbers whose sum is 174.
Find three consecutive numbers whose sum is 174.
Determine three consecutive even numbers whose sum is 222.
Determine three consecutive even numbers whose sum is 222.
What are three consecutive odd numbers whose sum is 177?
What are three consecutive odd numbers whose sum is 177?
Two cars start from the same point and travel in opposite directions. After 4 hours, they are 460 miles apart. If one car travels 15 mph faster than the other, what is the speed of the slower car?
Two cars start from the same point and travel in opposite directions. After 4 hours, they are 460 miles apart. If one car travels 15 mph faster than the other, what is the speed of the slower car?
A train leaves a station and travels north at 75 mph. Two hours later, a second train leaves on a parallel track traveling north at 125 mph. How long will it take the second train to overtake the first train?
A train leaves a station and travels north at 75 mph. Two hours later, a second train leaves on a parallel track traveling north at 125 mph. How long will it take the second train to overtake the first train?
Two cyclists start from cities 162 miles apart and cycle toward each other. If one cyclist travels at 8 mph and the other at 10 mph, how long will it take them to meet?
Two cyclists start from cities 162 miles apart and cycle toward each other. If one cyclist travels at 8 mph and the other at 10 mph, how long will it take them to meet?
A boat travels downstream (with the current) at 20 mph and upstream (against the current) at 12 mph. Find the speed of the boat in still water.
A boat travels downstream (with the current) at 20 mph and upstream (against the current) at 12 mph. Find the speed of the boat in still water.
Two buses leave from different cities that are 250 km apart and head towards each other. Bus A travels at a rate of 55 km/h, while Bus B travels at 45 km/h. If they both leave at the same time, after how many hours will they meet?
Two buses leave from different cities that are 250 km apart and head towards each other. Bus A travels at a rate of 55 km/h, while Bus B travels at 45 km/h. If they both leave at the same time, after how many hours will they meet?
An airplane flies from City A to City B in 3 hours with a tailwind. The return flight against the same wind takes 4 hours. If the distance between the cities is 1200 miles, what is the speed of the airplane in still air?
An airplane flies from City A to City B in 3 hours with a tailwind. The return flight against the same wind takes 4 hours. If the distance between the cities is 1200 miles, what is the speed of the airplane in still air?
A car travels 240 miles in the same time that a train travels 360 miles. If the speed of the train is 30 mph faster than the car, find the speed of the car.
A car travels 240 miles in the same time that a train travels 360 miles. If the speed of the train is 30 mph faster than the car, find the speed of the car.
Two hikers start at the same trailhead and hike in opposite directions. After 5 hours, they are 25 miles apart. If one hiker walks twice as fast as the other, find the speed of the slower hiker.
Two hikers start at the same trailhead and hike in opposite directions. After 5 hours, they are 25 miles apart. If one hiker walks twice as fast as the other, find the speed of the slower hiker.
A motorboat travels 48 miles downstream in 2 hours and returns upstream in 3 hours. What is the speed of the current?
A motorboat travels 48 miles downstream in 2 hours and returns upstream in 3 hours. What is the speed of the current?
Two friends live 270 miles apart. They start driving towards each other at the same time. One drives at 60 mph and the other at 75 mph. In how many hours will they meet?
Two friends live 270 miles apart. They start driving towards each other at the same time. One drives at 60 mph and the other at 75 mph. In how many hours will they meet?
A cyclist rides for 3 hours at a speed of 18 km/h and then for 2 hours at 22 km/h. What is the cyclist's average speed for the entire trip?
A cyclist rides for 3 hours at a speed of 18 km/h and then for 2 hours at 22 km/h. What is the cyclist's average speed for the entire trip?
Two cars start from the same city and travel in the same direction. One travels at 40 mph and the other at 55 mph. After how many hours will they be 75 miles apart?
Two cars start from the same city and travel in the same direction. One travels at 40 mph and the other at 55 mph. After how many hours will they be 75 miles apart?
A train leaves a station at 60 mph. Two hours later, a second train leaves the same station traveling in the same direction at 80 mph. How many hours will it take the second train to catch the first train?
A train leaves a station at 60 mph. Two hours later, a second train leaves the same station traveling in the same direction at 80 mph. How many hours will it take the second train to catch the first train?
Two planes start from the same airport and fly in opposite directions. One flies at 400 mph and the other at 500 mph. After how many hours will they be 2700 miles apart?
Two planes start from the same airport and fly in opposite directions. One flies at 400 mph and the other at 500 mph. After how many hours will they be 2700 miles apart?
A riverboat travels at 15 mph in still water. It travels 70 miles upstream against the current in 5 hours. What is the speed of the current?
A riverboat travels at 15 mph in still water. It travels 70 miles upstream against the current in 5 hours. What is the speed of the current?
Two cars start at the same time from the same place and travel in opposite directions. One travels at 45 mph and the other at 55 mph. After how many hours will they be 400 miles apart?
Two cars start at the same time from the same place and travel in opposite directions. One travels at 45 mph and the other at 55 mph. After how many hours will they be 400 miles apart?
A train leaves a station and travels at 50 mph. Two hours later, a faster train leaves from the same station on the same track and travels at 70 mph. How long does it take the faster train to overtake the slower train?
A train leaves a station and travels at 50 mph. Two hours later, a faster train leaves from the same station on the same track and travels at 70 mph. How long does it take the faster train to overtake the slower train?
Two runners start a race at the same time. One runs at 8 mph and the other at 10 mph. If the race is 5 miles long, how much sooner does the faster runner finish?
Two runners start a race at the same time. One runs at 8 mph and the other at 10 mph. If the race is 5 miles long, how much sooner does the faster runner finish?
Two buses start from the same station and travel in opposite directions. The first bus travels at 55 mph and the second bus travels at 65 mph. After how many hours will they be 600 miles apart?
Two buses start from the same station and travel in opposite directions. The first bus travels at 55 mph and the second bus travels at 65 mph. After how many hours will they be 600 miles apart?
A boat can travel 24 miles upstream in 4 hours. If the return trip downstream takes only 2 hours, what is the speed of the boat in still water?
A boat can travel 24 miles upstream in 4 hours. If the return trip downstream takes only 2 hours, what is the speed of the boat in still water?
Two trains are traveling towards each other from cities that are 330 miles apart. One train is traveling at 70 mph and the other is traveling at 40 mph. If they both leave at the same time, how long will it take them to meet?
Two trains are traveling towards each other from cities that are 330 miles apart. One train is traveling at 70 mph and the other is traveling at 40 mph. If they both leave at the same time, how long will it take them to meet?
A bus leaves a station and travels at 45 mph. One hour later, a car leaves the same station traveling at 60 mph in the same direction. How many hours will it take the car to catch the bus?
A bus leaves a station and travels at 45 mph. One hour later, a car leaves the same station traveling at 60 mph in the same direction. How many hours will it take the car to catch the bus?
Two cyclists start from the same point and travel in opposite directions. One cycles at 12 mph and the other at 15 mph. How long will it take them to be 81 miles apart?
Two cyclists start from the same point and travel in opposite directions. One cycles at 12 mph and the other at 15 mph. How long will it take them to be 81 miles apart?
A plane flies 600 miles with the wind in 2 hours and returns against the wind in 3 hours. What is the speed of the wind?
A plane flies 600 miles with the wind in 2 hours and returns against the wind in 3 hours. What is the speed of the wind?
Flashcards
How to approach word problems?
How to approach word problems?
Read the problem carefully to understand the scenario and question.
Determine the Unknown
Determine the Unknown
Identify what the problem is asking you to find. Assign variables.
Represent with Symbols
Represent with Symbols
Translate the words into math. Use symbols to represent quantities and relationships.
Apply Equality Properties
Apply Equality Properties
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Number Problem Example
Number Problem Example
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Sum of Two Numbers Example
Sum of Two Numbers Example
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Sum and Difference Example
Sum and Difference Example
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Consecutive Numbers Example
Consecutive Numbers Example
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Odd Consecutive Numbers
Odd Consecutive Numbers
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Consecutive Even Numbers
Consecutive Even Numbers
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Distance Problem: Buses Approaching
Distance Problem: Buses Approaching
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Buses Driving Opposite Directions
Buses Driving Opposite Directions
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Overtaking Vehicle Problem
Overtaking Vehicle Problem
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Trains Approaching
Trains Approaching
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Cars Diverging Problem
Cars Diverging Problem
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Taxi Overtaking Jeepney
Taxi Overtaking Jeepney
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Study Notes
- Lesson is on the application of linear equations to distance problems
- Learning objectives involve reading comprehension, problem solving, representing problems, using equality properties
Review: Number Problems
- If 25 is added to thrice a number, the result is 289; the number is 88, and the equation is 3x + 25 = 289
- The sum of two numbers is 287, and twice the smaller number is 10 less than the larger number; the smaller number is 99, the larger number is 188, with x + (2x - 10 ) = 287
- The sum of two numbers is 140 and their difference is 50; the numbers are 95 and 45, where x + y + x - y = 140 + 50
- The sum of three consecutive numbers is 240; the numbers are 79, 80, and 81, where x + x + 1+ x + 2 = 240 or 3x + 3 = 240
- The sum of three consecutive odd numbers is 141; the numbers are 45, 47 and 49, where x + x + 2 + x + 4 = 141 or 3x + 6 =141
- The sum of four consecutive even numbers is 284; the numbers are 68, 70, 72 and 74, where x + x + 2 + x + 4 + x + 6 = 284 or 4x + 12 = 284
Distance Problems
- Two buses leave at the same time from different provinces 200 km apart
- Bus A travels 5 km/h faster than Bus B and they meet after 2 hours
- Bus A is traveling at 52.5 km/h, and Bus B travels at 47.5 km/h, where 2(x + 5) + 2x = 200
- Two buses start at the same station and travel in opposite directions
- After 3 minutes, the buses are 10 km apart
- If one bus is 1 km per hour faster than the other bus, the Slower Bus travels at 99.5km/h and the Faster Bus travels at 100.5km/h, where X + X + = 10
- A car leaves a station traveling at 60km/h
- One hour later, a van leaves the same station traveling in the same direction at 80km/h
- The van overtakes the car after 3 hours where 60 ( x + 1 ) = 80 (x)
- Two trains leave at the same time from two different cities 300 km apart
- Train X travels at 4 km/h faster than train Y, and they meet after 3 hours
- Train Y travels at 48 km/h, and Train X travels at 52 km/h, by 3(x + 4) + 3x = 300
- Two cars start at the same station and travel in opposite directions
- After 1 hour, they are 24 km apart. If one car is 2 km per hour faster than the other car
- Slower Car travels at 11 km/h and Faster Car travels at 13 km/h where x + x + 2 = 24
- A jeepney leaves Ronnie's house at 40 km per hour
- Two hours later, a taxi leaves the same place at 50 km per hour
- The taxi overtakes the jeepney after 10 hours where 40x = 50 (x - 2)
- A bus leaves the station traveling at 60 km/h and one hour later; a car leaves the same station traveling at 80 km/h
- The car overtakes the bus after 4 hours.
- Two cyclists start from two different cities that are 180 km apart
- Cyclist A rides 4 km/h faster than cyclist B, and they meet after 3 hours
- Cyclist A rides at 32 km/h, and Cyclist B rides at 28 km/h
- Two cars leave the same station and travel in opposite directions
- After 2 hours, the cars are 160 km apart
- If one car is 2 km/h faster than the other car; Slower Car is traveling at 39 km/h, and Faster Car travels at 41 km/h
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