A motorist completes a journey of 1330 km in 14 hours. What is his average speed in kilometers per hour? How long will it take to cover a distance of 570 km at the same average spe... A motorist completes a journey of 1330 km in 14 hours. What is his average speed in kilometers per hour? How long will it take to cover a distance of 570 km at the same average speed?
Understand the Problem
The question requires calculating the average speed of a motorist given the total distance and time of a journey. Then, using this average speed, it asks to calculate the time it would take to cover a different distance. We first calculate the average speed by dividing total distance by total time. Then we calculate how long it will take to cover a distance of 570km by dividing the distance by the average speed.
Answer
(a) 60 km/h (b) 9.5 hours
Answer for screen readers
(a) The average speed of the motorist is 60 km/h. (b) It will take the motorist 9.5 hours to cover a distance of 570 km.
Steps to Solve
- Calculate the total time in hours
Convert the mixed fraction $2\frac{1}{2}$ to an improper fraction: $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$ hours. This is equal to 2.5 hours.
- Calculate the average speed
Average speed is calculated by dividing the total distance by the total time. $$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$ $$ \text{Average Speed} = \frac{150 \text{ km}}{2.5 \text{ hours}} = 60 \text{ km/h} $$
- Calculate the time to cover 570 km
Time is calculated by dividing the distance by the average speed. $$ \text{Time} = \frac{\text{Distance}}{\text{Average Speed}} $$ $$ \text{Time} = \frac{570 \text{ km}}{60 \text{ km/h}} = 9.5 \text{ hours} $$ So, it will take 9.5 hours to cover 570 km.
(a) The average speed of the motorist is 60 km/h. (b) It will take the motorist 9.5 hours to cover a distance of 570 km.
More Information
The average speed is a useful concept in physics and everyday life. It helps us estimate the time it takes to travel a certain distance, assuming a constant speed. In reality, speed often varies due to traffic, road conditions, and other factors.
Tips
A common mistake is to not convert the time to a decimal or improper fraction before calculating the average speed. Another mistake can be made with the formulas either switching the numerator and denominators, for example dividing time by distance instead of distance by time when calculating speed.
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