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?

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.

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kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-01-20T18:05:12+01:00

ANSWER
[tex]18 \: hours[/tex]

EXPLANATION

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

[tex] \frac{1}{4.5} = \frac{1}{ \frac{9}{2} } = \frac{2}{9} [/tex]

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

[tex] \frac{1}{6} [/tex]

If Pippin takes
[tex]x \: hours[/tex]
to do the work alone, then her working rate is

[tex] \frac{1}{x} [/tex]

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

This means that,

[tex] \frac{1}{x} + \frac{1}{6} = \frac{1}{4.5} [/tex]

or

[tex] \frac{1}{x} + \frac{1}{6} = \frac{2}{9} [/tex]

This implies that,

[tex] \frac{1}{x} = \frac{2}{9} - \frac{1}{6}[/tex]

We collect LCM on the right hand side to get,

[tex] \frac{1}{x} = \frac{4 - 3}{18} [/tex]

This simplifies to,

[tex] \frac{1}{x} = \frac{1}{18} [/tex]

We cross multiply to get,

[tex]18 = x[/tex]

Or

[tex]x = 18[/tex]

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