Why one method works and the other doesn't is my favourite type of question. It's a good test of your fundamentals.

CounterSniper and

royrijit1 allow me to reconcile the disparity between your respective approaches.

rahulkashyap this might help you understand as well.

Let us first review the fundamentals required to solve this question:

Theory: If the same distance is covered twice, but with different speeds then the average speed for the total trip = 2(S1*S2)/(S1+S2)

Speed = Distance / Time , As long as one of the factors ( speed , time or distance ) is constant you can equate the other 2.

i.e for the same distance S1/S2 = T2/T1

for the same speed D1/T1 = D2/T2

for the same time D1/S1 = D2/S2

Solution:Tanya's speed while travelling to the country club = S1

Tanya's speed while travelling back from the country club = S2

Average speed for the entire trip = 2(S1*S2)/(S1+S2)

As per the question, Average speed = 7/8 * S1

2(S1*S2)/(S1+S2) = 7/8 * S1 --> 16 * S2 = 7 * S1 + 7 * S2 --> 9*S2 = 7*S1

Since the distance, D, is constant for each trip --> S1/S2 = T2/T1 = 9/7

T2 = 50 * 9/7 = 64.28 mins ----Same as ---> T2 = 5/6 * 9/7 = 1.071 hrs

Lets us now review the approach used by

CounterSniper.

d1=s1*(5/6)

d2=s1*(7/8)*t

s1*5/6=s1*7/8*t -------> (here lies the problem)

if you solve the above you will get approx 57 mins.

Note the average speed = 7/8 S1 and not the speed for the return trip (S2). The above method makes it seem as if you are equating the distance for each trip, but incorrectly using 7/8S1 as the speed for the second trip.

If you want to use the average speed to solve the question, using the method mentioned above, then multiply the distance by 2 as the average speed is calculated for the same distance covered twice.

2 * s1*5/6 = s1*7/8*t

t = 1.904 hrs approx = 114.2 mins approx (This is the time for covering the distance twice. ie going to and coming from the country club)

Time taken to return from the country club = 114 - 50 = 64 mins

NOTICE: if you just multiply the incorrect answer of 57 mins by 2 you get 114 mins.

E is the correct answer.

- Light Yagami

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