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Two athletes cover the same distance at the rate of 10 and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.
- a)8.5 km
- b)750 km
- c)7.5 km
- d)15 km
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two athletes cover the same distance at the rate of 10 and 15 kmph res...
The distance travelled is 7.5 km.
Let the time taken by the athlete travelling at 10 kmph be t hours.
The time taken by the athlete travelling at 15 kmph is t -15/60 hours.
The distance travelled by both athletes is the same.
Therefore, 10t = 15(t -15/60)
Solving for t, we get t = 3/4 hours.
The distance travelled by both athletes is 10t = 10 * 3/4 = 7.5 km.
Most Upvoted Answer
Two athletes cover the same distance at the rate of 10 and 15 kmph res...
Given:
Rate of the first athlete = 10 kmph
Rate of the second athlete = 15 kmph
Let the time taken by the first athlete be t hours.
Then, the time taken by the second athlete = t - 1/4 hours (as the second athlete takes 15 minutes or 1/4 hours less than the first athlete)
To find:
The distance covered by both athletes is the same. Let this distance be d km.
Solution:
Using the formula, Distance = Speed × Time
Distance covered by the first athlete = 10t km
Distance covered by the second athlete = 15(t - 1/4) km
As both athletes cover the same distance, we can equate the above two distances.
10t = 15(t - 1/4)
10t = 15t - 15/4
Simplifying the above equation, we get:
5t = 15/4
t = 3/4
Substituting t = 3/4 in the formula for distance covered by the first athlete, we get:
Distance covered by the first athlete = 10 × 3/4 = 7.5 km
Therefore, the distance travelled by both athletes is 7.5 km. Hence, option (c) is the correct answer.
Rate of the first athlete = 10 kmph
Rate of the second athlete = 15 kmph
Let the time taken by the first athlete be t hours.
Then, the time taken by the second athlete = t - 1/4 hours (as the second athlete takes 15 minutes or 1/4 hours less than the first athlete)
To find:
The distance covered by both athletes is the same. Let this distance be d km.
Solution:
Using the formula, Distance = Speed × Time
Distance covered by the first athlete = 10t km
Distance covered by the second athlete = 15(t - 1/4) km
As both athletes cover the same distance, we can equate the above two distances.
10t = 15(t - 1/4)
10t = 15t - 15/4
Simplifying the above equation, we get:
5t = 15/4
t = 3/4
Substituting t = 3/4 in the formula for distance covered by the first athlete, we get:
Distance covered by the first athlete = 10 × 3/4 = 7.5 km
Therefore, the distance travelled by both athletes is 7.5 km. Hence, option (c) is the correct answer.
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