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 has two parts: first, calculate the motorist's average speed given the distance and time of the journey. Second, calculate the time it will take to cover a different distance at the same average speed.
Answer
Average speed: $60 \text{ km/h}$. Time to cover 270 km: $4.5 \text{ hours}$.
Answer for screen readers
The average speed of the motorist is $60 \text{ km/h}$. It will take $4.5 \text{ hours}$ to cover 270 km at the same average speed.
Steps to Solve
- Calculate average speed
To find the average speed, divide the total distance traveled by the total time taken.
$$ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} $$
Given the total distance is 150 km and the total time is 2.5 hours:
$$ \text{Average speed} = \frac{150 \text{ km}}{2.5 \text{ hours}} $$
- Compute the average speed
Divide 150 by 2.5
$$ \text{Average speed} = 60 \text{ km/h} $$
- Calculate the time to cover 270 km
To find the time it takes to cover 270 km at the same average speed, divide the distance by the average speed.
$$ \text{Time} = \frac{\text{Distance}}{\text{Average speed}} $$
Given the distance is 270 km and the average speed is 60 km/h:
$$ \text{Time} = \frac{270 \text{ km}}{60 \text{ km/h}} $$
- Compute the time
Divide 270 by 60
$$ \text{Time} = 4.5 \text{ hours} $$
The average speed of the motorist is $60 \text{ km/h}$. It will take $4.5 \text{ hours}$ to cover 270 km at the same average speed.
More Information
The average speed is a scalar quantity, meaning it only has magnitude and no direction.
Tips
A common mistake is to mix up the distance and time when calculating speed or time. Always ensure you are dividing the distance by the time to find the speed, and dividing the distance by the speed to find the time. Another common mistake is to not include units in your calculations or final answer.
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