Question

Working together, merry and pippin can build a wall in 4.5 hours. if merry can do the job alone in 6 hours working alone, how long would it take pippin to build the wall when working alone?

Answer 1

Merry builds 100% wall for 6 hours. For 4.5 hours she did 75% of wall (4.5 * 100 /6) , rest 25% did another girl for 4.5 hours. If she builds wall alone she would spend 18 hours.

Answer 2

ANSWER
$18 \: hours$

EXPLANATION

If Merry and Pippin can build a wall in 4.5 hours, their working rate is

$\frac{1}{4.5} = \frac{1}{ \frac{9}{2} } = \frac{2}{9}$

If Merry can do the work alone in 6 hours, then her rate of working is,

$\frac{1}{6}$

If Pippin takes
$x \: hours$
to do the work alone, then her working rate is

$\frac{1}{x}$

If we add their individual rates it should give us their combined rate.

This means that,

$\frac{1}{x} + \frac{1}{6} = \frac{1}{4.5}$

or

$\frac{1}{x} + \frac{1}{6} = \frac{2}{9}$

This implies that,

$\frac{1}{x} = \frac{2}{9} - \frac{1}{6}$

We collect LCM on the right hand side to get,

$\frac{1}{x} = \frac{4 - 3}{18}$

This simplifies to,

$\frac{1}{x} = \frac{1}{18}$

We cross multiply to get,

$18 = x$

Or

$x = 18$

Therefore it would take Pippin, 18 hours to build the wall when working alone.