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A motor cyclist participant of a race says We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 15 miles per hour. What was their average speed in the whole journey?
  • a)
    16 miles per hour
  • b)
    12 miles per hour
  • c)
    14 miles per hour
  • d)
    10 miles per hour
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A motor cyclist participant of a race says We drove with the speed of ...
Let the distance be d miles.
Time taken in the first lap =  d/10 hr
Time taken in the second lap = d/15 hr
Total distance traveled = 2d miles
Total time taken = d/10 + d/15 hr
Average speed = total distance/ total time
= 2d/(d/10 + d/15) = 2*10*15/(15 + 10) = 300/25 = 12 miles/hr
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Most Upvoted Answer
A motor cyclist participant of a race says We drove with the speed of ...
Given information:
- The motor cyclist drove with a speed of 10 miles per hour one way.
- While returning, they drove on the same route with a speed of 15 miles per hour.

To find:
The average speed of the whole journey.

Approach:
To find the average speed, we can use the formula:
Average speed = Total distance / Total time

Calculation:
Let's assume the distance traveled one way is 'd' miles.

Distance:
- The distance traveled one way is 'd' miles.
- Therefore, the total distance traveled in the whole journey is 2d miles (as the motor cyclist returns back using the same route).

Time:
- The time taken to travel one way at a speed of 10 miles per hour is d/10 hours (as time = distance/speed).
- The time taken to return at a speed of 15 miles per hour is d/15 hours.

Total time:
- The total time taken for the whole journey is (d/10) + (d/15) hours.

Average speed:
- Average speed = Total distance / Total time
- Average speed = 2d / [(d/10) + (d/15)]
- Simplifying the expression, we get:
Average speed = 2d / [(3d + 2d) / 30]
Average speed = 2d / (5d / 30)
Average speed = 2d * (30 / 5d)
Average speed = 60 / 5
Average speed = 12 miles per hour

Therefore, the average speed of the whole journey is 12 miles per hour, which corresponds to option 'B'.
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Community Answer
A motor cyclist participant of a race says We drove with the speed of ...
Let the distance be d miles.
Time taken in the first lap =  d/10 hr
Time taken in the second lap = d/15 hr
Total distance traveled = 2d miles
Total time taken = d/10 + d/15 hr
Average speed = total distance/ total time
= 2d/(d/10 + d/15) = 2*10*15/(15 + 10) = 300/25 = 12 miles/hr
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Question Description
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