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

Question

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

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

CounterSniper · Answer

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

generis · Answer

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

EgmatQuantExpert · Answer

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

JeffTargetTestPrep · Answer

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

archana89 · Answer

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

bumpbot · Answer

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

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