Percy can mow 1/a of a lawn in half an hour. Mona and Percy working together at their respective rates can mow the entire lawn in a couple of hours. How many minutes will Mona take to mow the lawn?
: Choice A.
Percy can mow 1/a of the lawn in 30 minutes
So, Percy can mow the lawn completely in 30a minutes.
Therefore, in 1 minute, Percy will mow 1/30a of the lawn.
Percy and Mona, together, can mow the lawn in 120 minutes.
So, together they mow 1/120 of the lawn.
If Mona alone can mow the lawn in M minutes, then 1/30a + 1/M = 1/120
Or 1/M = 1/120 - 1/30a
1/M = (a - 4)/120a
Or M = 120a/(a - 4).
Alternative way to solve this question.
Assume a value for a. Say a = 5.
So, Percy mows 1/5th of the lawn in 30 minutes.
Percy can mow the entire lawn in 150 minutes.
Percy and Mona mow the lawn in 120 minutes
So, if Mona takes M minutes to mow the lawn, 1/150 + 1/M = 1/120
Or 1/M = 1/120 - 1/150 = 1/600
Or M = 600.
Substitute a = 5 in the answer choices and check which of the answer choices results in 600.
Choice A : M = 120a/(a - 4)
If a = 5, we get M = 120*5/(5 - 4) = 600.
So, choice A is the correct answer.