Question

Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?

Answer 1

The correct answer is:

0.4 of the job.

Explanation:

Since Katherine can complete the job (100%, or 1) in 10 hours, she can complete 1/10 of it in 1 hour.

Both women together can complete the job in 2 hours. This means Katherine's rate multiplied by 2 hours, 0.1(2), added to Marina's rate multiplied by 2 hours, r*2, equal the entire job (100%, or 1 whole):

0.1(2)+r(2) = 1

0.2+2r = 1

Subtract 0.2 from each side:

0.2+2r-0.2 = 1-0.2

2r = 0.8

Divide each side by 2:

2r/2 = 0.8/2

r = 0.4

Marina's rate is 0.4 of the job per hour.

Answer 2

So, Katherine can do 0.1 of the job per hour. (if she needs 10 hours for the job, each hour she can do the whole divided by the time, so 1/10, which is 0.1)

if in two hours she and Marina can be done, then Marina will do 1(the whole job)-2/10 (twice as much as she can do in an hour)=0.8 of the job. So if Marina does 0.8 of the job in two hours, each hour she will do half of it: 0.4 - and this is the correct answer