1972 AMC 12 Problem 15

Question

A contractor estimated that one of his two bricklayers would take

9

hours to build a certain wall and the other

10

hours. However, he knew from experience that when they worked together, their combined output fell by

10

bricks per hour. Being in a hurry, he put both men on the job and found that it took exactly

5

hours to build the wall. The number of bricks in the wall was:

500

550

900

950

960

Let

N

be the number of bricks in the wall

Their actual combined hourly rate is

\frac{N}{9}+\frac{N}{10}-10

If the wall contains

N

bricks, the individual rates are

\frac{N}{9}

and

\frac{N}{10}.

Thus

5\left(\frac N9+\frac N{10}-10\right)=N.

Multiplying by

18

and simplifying gives

19N-900=18N,

hence

N=900.

Therefore, the correct answer is C.

Problem 15 in other years