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 asks for two calculations: first, to determine the average speed of a motorist given the distance and time of a journey, and second, to calculate the time it would take to cover a different distance at that same average speed. We'll use the formula: Average Speed = Total Distance / Total Time, and Time = Distance / Average Speed.
Answer
Average speed: $75$ km/h. Time to cover $300$ km: $4$ hours.
Answer for screen readers
The average speed of the motorist is $75$ km/h, and the time it would take to cover $300$ km at that speed is $4$ hours.
Steps to Solve
- Calculate the average speed
To find the average speed, we divide the total distance by the total time. $$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$ Given the total distance is $225$ km and the total time is $3$ hours: $$ \text{Average Speed} = \frac{225 \text{ km}}{3 \text{ hours}} = 75 \text{ km/h} $$
- Calculate the time to cover 300 km
To find the time it would take to cover $300$ km at the same average speed, we divide the distance by the average speed. $$ \text{Time} = \frac{\text{Distance}}{\text{Average Speed}} $$ Given the distance is $300$ km and the average speed is $75$ km/h: $$ \text{Time} = \frac{300 \text{ km}}{75 \text{ km/h}} = 4 \text{ hours} $$
The average speed of the motorist is $75$ km/h, and the time it would take to cover $300$ km at that speed is $4$ hours.
More Information
The average speed of $75$ km/h is a common speed on highways. The time of $4$ hours to cover $300$ km is a reasonable driving time for long journeys.
Tips
A common mistake is to mix up the formulas for speed and time, or to use the wrong units. For example, forgetting to convert minutes to hours, or using meters instead of kilometers. Always double-check that the units are consistent and that the formulas are applied correctly!
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