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# A byciclist travels up the hill at 10 miles per hour

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A byciclist travels up the hill at 10 miles per hour [#permalink]  29 Jun 2020, 05:33
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90% (01:19) correct 9% (00:25) wrong based on 11 sessions
A bicyclist travels up the hill at 10 miles per hour and returns down the same hill at 30 miles per hour. What is his/her average speed, in miles per hour, for the entire journey up and down the hill ?

A. 15

B. 17

C. 20

D. 22

E. 25
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
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Kudos [?]: 2982 [0], given: 11200

Re: A byciclist travels up the hill at 10 miles per hour [#permalink]  29 Jun 2020, 05:33
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Re: A byciclist travels up the hill at 10 miles per hour [#permalink]  29 Jun 2020, 10:06
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Let the distance one way = D

Average Speed = \frac{Total Distance}{Total Time}

Time uphill = $$\frac{D}{10}$$

Time downhill = $$\frac{D}{30}$$

Total time = $$\frac{D}{10} + \frac{D}{30} = \frac{30D+10D}{30 \times 10} = \frac{40D}{300}$$

Total Distance $$= D + D = 2D$$

Average Speed = $$2D / \frac{40D}{300} = \frac{2D \times 300}{40} = 15$$

OA, A
Carcass wrote:
A bicyclist travels up the hill at 10 miles per hour and returns down the same hill at 30 miles per hour. What is his/her average speed, in miles per hour, for the entire journey up and down the hill ?

A. 15

B. 17

C. 20

D. 22

E. 25

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If you like my solution, do give kudos!

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Joined: 19 Jan 2020
Posts: 11
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Kudos [?]: 5 [0], given: 26

Re: A byciclist travels up the hill at 10 miles per hour [#permalink]  02 Jul 2020, 08:21
Assume the one way distance as 30 miles (as it gives integers when calculating the time taken for each trip):

Time Uphill: ( 30/10 ) = 3hrs.

Time Downhill ( 30/30 ) = 1 hr

Therefore, Avg. Speed = 30(uphill) + 30(Downhill) / ( 3 + 1 ) = 60/4 = 15
Re: A byciclist travels up the hill at 10 miles per hour   [#permalink] 02 Jul 2020, 08:21
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