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

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Bunuel
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A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink] New post   23 Jul 2018, 00:21
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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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A
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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink] New post   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] New post   23 Jul 2018, 14:12
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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

Answer A
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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink] New post   23 Jul 2018, 22:59
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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.

Answer: 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] New post   25 Jul 2018, 17:30
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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

Answer: A
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Re: A bicyclist travels uphill from town A to town B for 2 hours at an ave [#permalink] New post   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
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Re: Average speed [#permalink] New post   23 Jan 2021, 09:10
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Re: Average speed [#permalink]
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