2420.62 – Brick Wall

Tim has employed Kim and Nim as bricklayers for the summer. Jim wants a brick path leading from the street, through his garden, to the side door. Tim estimates that Nim could build the wall in 9 hours and Kim could build it in 10. However, he has learned that when they work together, their combined output decreases by 10 bricks per hour. Nevertheless, being in a hurry, he puts them both to work on it and finds that it takes them exactly 5 hours, working together, to finish the path. How many bricks are in the path?

Solution

Let $b$ be the number of bricks in the wall.

In one hour, $N = \frac{b}{9}$ and $K = \frac{b}{10}$ .

Together, their hourly rate is $\frac{b}{9}+\frac{b}{10}-10$ .

And 5( $\frac{b}{9}+\frac{b}{10}-10$ ) = $b$

$\rightarrow\frac{5b}{9}+\frac{5b}{10}-50$ = $b$

$\rightarrow\frac{50b+45b}{90}-b =50$

$\rightarrow\frac{95b}{90}-b=50$

$\rightarrow\frac{5b}{90}=50$

$\rightarrow b=\frac{50\cdot90}{5}=900$ .