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A cyclist climbs a hill with a length of 400 m with a speed of

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A cyclist climbs a hill with a length of 400 m with a speed of  [#permalink]

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New post 26 Dec 2018, 20:16
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Question Stats:

74% (02:04) correct 26% (02:42) wrong based on 57 sessions

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A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?

A. 100 Seconds

B. 200 Seconds

C. 300 Seconds

D. 400 Seconds

E. 500 Seconds

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Re: A cyclist climbs a hill with a length of 400 m with a speed of  [#permalink]

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New post 27 Dec 2018, 04:23
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If the Question is Speed (coming down) = Two Times of Speed (going up)
While going up the time taken is d/s (Distance/speed)
while coming down time taken is d/2s (Speed is 2 times => 2 times of the speed while going up)

Total time = d/s + d/(2s) = 3d/(2s)

d= 400m = 0.4km
s = 7.2 km/hr

time = 3d/(2s) = 3*0.4 / (2*7.2) hr = 12/(2*72) hr = 1*3600/12 sec = 300s

So, Answer is C

If the Question is Speed (coming down) = Two Times greater than Speed (going up)
While going up the time taken is d/s (Distance/speed)
while coming down time taken is d/3s (Speed is 2 times greater => 3 times of the speed while going up)

Total time = d/s + d/(3s) = 4d/(3s)

d= 400m = 0.4km
s = 7.2 km/hr

time = 4d/(3s) = 4*0.4 / (3*7.2) hr = 16/(3*72) hr = 16*3600/(3*72) sec = 16*50/3 sec = 800/3 sec = 267 sec
So, either the questions needs to be updated or 267 has to be added as an option choice!

Hope it helps!
fitzpratik wrote:
A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?

A. 100 Seconds

B. 200 Seconds

C. 300 Seconds

D. 400 Seconds

E. 500 Seconds

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Re: A cyclist climbs a hill with a length of 400 m with a speed of  [#permalink]

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New post 04 Jun 2019, 23:51
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fitzpratik wrote:
A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?


We can solve this by converting units to m/s:

7.2 km/h = 7.2 * 1000 * 1/60 * 1/60 = 2m/s

Provided the question means to say 'speed when descending is twice the speed of climb'
we have,

t= 400/2 + 400/4 = 300m/s

Option C
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Re: A cyclist climbs a hill with a length of 400 m with a speed of   [#permalink] 04 Jun 2019, 23:51
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