A can do a piece of work in 9 days. B is 50% more efficient than A. The number of days it takes B to do the same piece of work is:

1951 AMC 12 Problem 13

Attempt Problem 13 of the 1951 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1951 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

13.

A

can do a piece of work in

9

days.

B

50\%

more efficient than

A.

The number of days it takes

B

to do the same piece of work is:

13\dfrac12

4\dfrac12

6

3

None of these answers

Translate days per job into jobs per day

Multiply

A

’s rate

\frac{1}{9}

1.5

A

’s rate is

\frac{1}{9}

job per day. Thus

B

’s rate is

\frac32\cdot\frac19=\frac16

job per day, so

B

needs

6

days.

Thus, the correct answer is C.