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 570km at the same average spee... 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 570km at the same average speed?
Understand the Problem
The question is in two parts. First, calculate the average speed in kilometers per hour given the total distance and time. Second, using that average speed, calculate the time it would take to cover a different distance.
Answer
(a) $60$ km/h (b) $4.5$ hours
Answer for screen readers
(a) The average speed is $60$ km/h.
(b) The time it would take to cover $270$ km is $4.5$ hours, or $4$ hours and $30$ minutes.
Steps to Solve
- Calculate the average speed
To calculate the average speed, divide the total distance by the total time. The total distance is 150 km and the total time is 2 hours and 30 minutes. Convert the time to hours: 30 minutes is 0.5 hours, so the total time is 2.5 hours.
$$ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} $$
$$ \text{Average speed} = \frac{150 \text{ km}}{2.5 \text{ hours}} $$
$$ \text{Average speed} = 60 \text{ km/h} $$
- Calculate the time to cover 270 km
To find the time it would take to cover 270 km at the average speed of 60 km/h, divide the distance by the speed.
$$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$
$$ \text{Time} = \frac{270 \text{ km}}{60 \text{ km/h}} $$
$$ \text{Time} = 4.5 \text{ hours} $$
- Convert the time to hours and minutes
Convert 4.5 hours to hours and minutes. The 4 represents 4 full hours, and the 0.5 represents half an hour, which is 30 minutes. Therefore, the time is 4 hours and 30 minutes.
(a) The average speed is $60$ km/h.
(b) The time it would take to cover $270$ km is $4.5$ hours, or $4$ hours and $30$ minutes.
More Information
The formula relating distance, speed, and time is $d = st$, where $d$ is distance, $s$ is speed, and $t$ is time. This formula can be rearranged to solve for any of the variables if the other two are known.
Tips
A common mistake is to not convert the minutes into hours correctly when calculating the average speed. For example, using 2.3 hours instead of 2.5 hours for 2 hours and 30 minutes. Doing this will lead to an incorrect average speed and subsequently an incorrect time calculation.
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