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# A bicyclist travels uphill from town A to town B for 2 hours at an ave

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Joined: 02 Sep 2009
Posts: 50002
A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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23 Jul 2018, 00:21
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:36) correct 13% (02:45) wrong based on 48 sessions

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A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5
(B) 5
(C) 26/5
(D) 27/5
(E) 28/5

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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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23 Jul 2018, 00:33
Bunuel wrote:
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5
(B) 5
(C) 26/5
(D) 27/5
(E) 28/5

distance between A and B = 2*4=8 miles
time taken by the cyclist to return from B to A = 8/6 hour

total time taken = 2+8/6=20/6 hour
average speed = distance /total time =16*6/20=24/5

or the same thing can be done by this simple formula
2xy/x+y
where x and y are two speeds
2*6*4/6+4
24/5
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A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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23 Jul 2018, 14:12
Bunuel wrote:
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5
(B) 5
(C) 26/5
(D) 27/5
(E) 28/5

Average speed = $$\frac{TotalDistance}{TotalTime}$$

(1) Distance between A and B
From Leg 1, $$D=r*t$$
$$D=(4mph*2hrs)=8$$ miles

(2) Time, $$t_2$$, taken for Leg 2 at 6 mph? D = 8
$$(t_2*6)=8$$ miles
$$t_2=\frac{8}{6}=\frac{4}{3}$$ hours

(3) Average speed
Total distance: $$(8 + 8) = 16$$ miles
Total time: $$(2+\frac{4}{3})=(\frac{6}{3}+\frac{4}{3})=\frac{10}{3}$$ hours

Average speed: $$\frac{16}{(\frac{10}{3})}=(16*\frac{3}{10})=\frac{24}{5}$$ mph

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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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23 Jul 2018, 22:59

Solution

Given:
• A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour
• The bicyclist returns along the same road at an average speed of 6 miles per hour

To find:
• The bicyclist’s average speed for the round trip, in miles per hour

Approach and Working:
In the uphill and downhill journey, the distance covered remains constant.

We know if a journey is divided into two equidistant parts, and they are covered at a speed of a and b respectively,
• Then the average speed throughout the journey = $$\frac{2ab}{a+b}$$

• Hence, the average speed in this case = $$\frac{2 * 4 * 6}{(4 + 6)} = \frac{24}{5}$$ miles per hour

Hence, the correct answer is option A.

Article on same concept: Application of Average Speed in Distance problems
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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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25 Jul 2018, 17:30
Bunuel wrote:
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5
(B) 5
(C) 26/5
(D) 27/5
(E) 28/5

We can use the average rate formula:

average = total distance/total time

average = 2d/(d/4 + d/6)

average = 2d/(3d/12 + 2d/12)

average = 2d/(5d/12) = 24d/5d = 24/5

Alternate Solution:

We see that the distance from town A to town B is 2 x 4 = 8 miles, and thus the round trip distance is 16 miles. We can use the average rate formula:

average = total distance/total time

average = 16/(8/4 + 8/6)

average = 16/(2 + 8/6)

average = 16/(20/6)

average = 16/(10/3)

average = 48/10 = 24/5 = 4 4/5

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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave  [#permalink]

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26 Jul 2018, 01:57
Bunuel wrote:
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same roadat an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?

(A) 24/5
(B) 5
(C) 26/5
(D) 27/5
(E) 28/5

Sometimes, it's better to solve Rate/Work questions using below chart/table:

Rate X Time = Distance
4m/hr 2hrs 8 miles (Speed * Time = Distance)
6m/hr ?? 8 miles (Reason: Highlighted above)
----------------------------------
Time = 8 miles/ 6 m/hr = 8/6 hr

Hence, the Average speed = Total Distance / Total Time
= (8+8) / (2+8/6)
= 16 * 6 /20
= 24/5 Hence, Answer is option A
Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave &nbs [#permalink] 26 Jul 2018, 01:57
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