Podcast
Questions and Answers
What is the usual time it takes for the train to reach its destination?
What is the usual time it takes for the train to reach its destination?
If the total distance between the two people is 276 km, and the difference in their speeds is 5 km/h, what is the speed of the faster person?
If the total distance between the two people is 276 km, and the difference in their speeds is 5 km/h, what is the speed of the faster person?
What is the speed of the slower person?
What is the speed of the slower person?
If the train's usual speed is $s$ km/h, how long does it take to reach its destination when traveling at 1/3 of its usual speed?
If the train's usual speed is $s$ km/h, how long does it take to reach its destination when traveling at 1/3 of its usual speed?
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What is the total distance traveled by the two people?
What is the total distance traveled by the two people?
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If two automobiles are 276 kilometres apart and start to travel toward each other at the same time, with the faster car's speed being 5 km/h more than the slower car's speed, and they meet after 6 hours, what is the rate of the faster car?
If two automobiles are 276 kilometres apart and start to travel toward each other at the same time, with the faster car's speed being 5 km/h more than the slower car's speed, and they meet after 6 hours, what is the rate of the faster car?
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If a car travels at a constant speed of 60 km/h for 2 hours, then at a constant speed of 80 km/h for 3 hours, what is the total distance the car has traveled?
If a car travels at a constant speed of 60 km/h for 2 hours, then at a constant speed of 80 km/h for 3 hours, what is the total distance the car has traveled?
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A car travels at a constant speed of $x$ km/h for the first 3 hours and then at a constant speed of $y$ km/h for the next 2 hours. If the total distance traveled is 450 km, what is the value of $x + y$?
A car travels at a constant speed of $x$ km/h for the first 3 hours and then at a constant speed of $y$ km/h for the next 2 hours. If the total distance traveled is 450 km, what is the value of $x + y$?
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A person walks at a constant speed of 4 km/h for the first 2 hours and then runs at a constant speed of 8 km/h for the next 3 hours. What is the total distance the person has traveled?
A person walks at a constant speed of 4 km/h for the first 2 hours and then runs at a constant speed of 8 km/h for the next 3 hours. What is the total distance the person has traveled?
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Two cars start from the same point and travel in opposite directions. Car A travels at a constant speed of 60 km/h, while Car B travels at a constant speed of 80 km/h. If they meet after 2 hours, what is the total distance traveled by both cars?
Two cars start from the same point and travel in opposite directions. Car A travels at a constant speed of 60 km/h, while Car B travels at a constant speed of 80 km/h. If they meet after 2 hours, what is the total distance traveled by both cars?
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Study Notes
Time, Speed, and Distance Word Problems
Introduction
Word problems involving time, speed, and distance are common in various fields such as math, physics, and everyday life situations. These problems often require understanding the relationships between speed, distance, and time, as well as being able to apply algebraic principles to solve them.
Basic Concepts
Before delving into the challenging questions, let's review some basic concepts:
- Speed: Speed is the rate at which an object moves or travels. It is usually measured in meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).
- Distance: Distance is the amount of space traveled between two points. It is typically measured in meters (m), kilometers (km), or miles (mi).
- Time: Time is the duration between two events. It is usually measured in seconds (s), minutes, hours (h), or days.
Tough Questions
Now let's tackle some difficult questions that require understanding and applying the relationship between speed, distance, and time:
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Two automobiles are 276 kilometres apart and start to travel toward each other at the same time. They travel at rates differing by 5 km/h. If they meet after 6 hours, find the rate of each.
Let x be the faster car's speed and y be the slower car's speed. We know that they meet after 6 hours, so we can set up the equation:
x + y = 276 (since their total distance traveled is equal to the initial distance between them)
We also know that the difference between their speeds is 5 km/h, so we can set up another equation:
x - y = 5
Solving these two equations simultaneously, we find that x = 45 km/h and y = 40 km/h.
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A train is going at 1/3 of its usual speed and it takes an extra 30 minutes to reach its destination. Find its usual time to cover the same distance.
Let s be the usual speed of the train and t be the time it takes to reach the destination when traveling at 1/3 of its usual speed. We know that the train takes 30 minutes longer to reach its destination, so we can set up the equation:
s/3 * t + 30 = st (since the usual time to reach the destination is t)
Simplifying and solving for t, we find that t = 5 hours.
These questions demonstrate the importance of understanding the relationships between speed, distance, and time, as well as the ability to apply algebraic principles to solve real-life scenarios.
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Description
Explore word problems involving time, speed, and distance, commonly found in math, physics, and daily life scenarios. Learn the fundamental concepts of speed, distance, and time measurement, and practice solving challenging questions that require applying algebraic principles to find solutions.
