Question

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?

Answer 1

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 `4/3xx2=8/3` hours, which boils down to 2 hours and 20 minutes.

Answer 2

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 `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 + 1/3 larr color(brown)(" 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 `1/3` Henries to complete the task.

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

`[color(white)(2/3)1" Henries "xx2" hours "]+ [1/3" Henries "xx2" hours"]`

Consequently Henry would need to work for `" "1 1/3xx2" hours"`

But

`" "2" hours "xx1 1/3" " =" " 2 2/3" hours "=` 2 hours 40 minutes