It takes the owner\operator of a dog kennel 2 hr to clean all of the cages. It takes his assistant 1 hr more than that to clean the same cages. How long will it take if they work together?
A) $2 \frac { 1 } { 5 } \mathrm { hr }$
B) $1 \frac { 3 } { 5 } \mathrm { hr }$
C) $1 \frac { 1 } { 5 } \mathrm { hr }$
D) $3 \frac { 1 } { 5 } \mathrm { hr }$
E) $1 \frac { 1 } { 3 } \mathrm { hr }$

Question

Quizplus · Accepted Answer

Let's start by finding how much each person can clean in an hour:
- Owner/operator: 1/2 cages/hr
- Assistant: 1/(2+1) cages/hr = 1/3 cages/hr

Working together, they can clean:
1/2 cages/hr + 1/3 cages/hr = 5/6 cages/hr

To clean all the cages, they need to work for:
total number of cages ÷ cages/hr = 1 ÷ (5/6) = 6/5 hours

Therefore, it will take them 1 1/5 hr to clean all of the cages if they work together.

It Takes the Owner\operator of a Dog Kennel 2 Hr 215hr2 \frac { 1 } { 5 } \mathrm { hr }251​hr

It Takes the Owner\operator of a Dog Kennel 2 Hr $2 \frac { 1 } { 5 } \mathrm { hr }$