It takes a grounds keeper 45 minutes to prepare a softball field for a game. It takes his assistant 65 minutes to prepare the same field. How long will it take if they work together to prepare the field?
A) $24 \frac { 13 } { 22 } \mathrm {~min}$
B) $26 \frac { 13 } { 21 } \mathrm {~min}$
C) $25 \frac { 13 } { 22 } \mathrm {~min}$
D) $26 \frac { 13 } { 22 } \mathrm {~min}$
E) $26 \frac { 15 } { 22 } \mathrm {~min}$

Question

Quizplus · Accepted Answer

Let t be the time it takes them to work together. Then their combined rate of work is 1/t, and the amount of work done by the grounds keeper is 1/45 and the amount of work done by the assistant is 1/65. Thus, we have the equation:

1/45 + 1/65 = 1/t

To solve for t, we first find a common denominator on the left side:

(65 + 45)/(45*65) = 1/t

110/2925 = 1/t

Multiplying both sides by 2925 gives:

t = 2925/110 = 26 13/22 minutes

Therefore, the answer is D.

It Takes a Grounds Keeper 45 Minutes to Prepare a Softball