Problem Solving

BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:43 am

If Carol can finish a job in 5 hours and Steve can finish the same job in 10 hours, how many minutes will it take both of them together to finish the job?

A. 160
B. 180
C. 200
D. 210
E. 220

Answer: C
Source: Kaplan

GIVEN:
Carol can finish a job in 5 hours
Steve can finish the same job in 10 hours

A useful approach is to assign a "nice" value to the job.
We want a value that works well with the given information (5 hours and 10 hours).
So, let's say the entire job requires 10 tasks

This means Carol can complete 10 tasks in 5 hours. So, Carol's RATE = 2 tasks per hour
Similarly, Steve can complete 10 tasks in 10 hours. So, Steve's RATE = 1 tasks per hour

So their, COMBINED rate = 2 + 1 = 3 tasks per hour

How many minutes will it take both of them together to finish the job?
Time = output/rate
So, time = 10/3 = 10/3 HOURS

10/3 HOURS = (10/3)(60) MINUTES
= 200 MINUTES

Answer: C

Cheers,
Brent

BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:43 am

If Carol can finish a job in 5 hours and Steve can finish the same job in 10 hours, how many minutes will it take both of them together to finish the job?

A. 160
B. 180
C. 200
D. 210
E. 220

Answer: C

Solution:

The rate of Carol is 1/5 of the job per hour and Steven 1/10 of the job per hour. Therefore, the time needed for both of them together to finish the job is 1/(1/5 + 1/10) = 1/(2/10 + 1/10) = 1/(3/10) = 10/3 hours, or 10/3 x 60 = 200 minutes.

Answer: C