# Henry can clean the pool three times as fast as John. Together they can do the job in 2 hours. About how long would it take Henry to clean the pool alone?

Nov 5, 2016

A matter of ratios.

#### Explanation:

In the two hours it took them H did three times as much as J.
So the two hours worth of work is split 3:1.
H has done 3/4 of the work in 2 hours, so he could do the whole pool by himself in 4/3 of the time, or $\frac{4}{3} \times 2 = \frac{8}{3}$ hours, which boils down to 2 hours and 20 minutes.

Nov 9, 2016

Henry would take 2 hour 40 minute to complete the task on his own.

#### Explanation:

This type of question is sometimes a bit difficult to untangle.

The initial condition is that:

John's work rate is $\frac{1}{3}$ the work rate of Henry's

The total time for both to complete the task when working together is 2 hours.
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Using the fact that each contribute work for the period of 2 hours.

Lets try and put this into a model.

Standardising the amount of work done by Henry as 1

Then the total amount of work expressed in the rate of Henry is

$1 + \frac{1}{3} \leftarrow \textcolor{b r o w n}{\text{ where the "1/3" work quantity came from John}}$

Lets be silly for a moment in invent a unit of work called a 'Henries'

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This does not really exist. Unless you go back in time and in which case it was used as a unit of magnetic flux generated in a coil. I think!.
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So the total amount of work that Henry could do in 2 hours if he worked on his own is 1 Henries. He will need to add to this $\frac{1}{3}$ Henries to complete the task.

So the total work needed to complete the task is generated by:

$\left[\textcolor{w h i t e}{\frac{2}{3}} 1 \text{ Henries "xx2" hours "]+ [1/3" Henries "xx2" hours}\right]$

Consequently Henry would need to work for $\text{ "1 1/3xx2" hours}$

But

$\text{ "2" hours "xx1 1/3" " =" " 2 2/3" hours } =$ 2 hours 40 minutes