Jake can wash a car in 40 minutes, while Harold can wash the same car in 50 minutes. How long will it take them to wash the car if they work together?
A) $\quad 40$ minutes
B) $\frac { 9 } { 200 }$ minutes
C) 10 minutes
D) $\quad 30$ minutes
E) $\quad \frac { 200 } { 9 }$ minutes

Question

Jake can wash a car in 40 minutes, while Harold can wash the same car in 50 minutes. How long will it take them to wash the car if they work together? 
A) $\quad 40$ minutes
B) $\frac { 9 } { 200 }$ minutes
C) 10 minutes
D) $\quad 30$ minutes
E) $\quad \frac { 200 } { 9 }$ minutes

Quizplus · Accepted Answer

Jake's rate is $1/40$ cars per minute, and Harold's rate is $1/50$ cars per minute. Together, their rate is $(1/40 + 1/50)$ cars per minute, which simplifies to $(5/200 + 4/200) = 9/200$ cars per minute. To find the time taken to wash one car, take the reciprocal of their combined rate, which is $(200/9)$ minutes.

Jake Can Wash a Car in 40 Minutes, While Harold 40\quad 4040

Jake Can Wash a Car in 40 Minutes, While Harold $\quad 40$