SOLUTION: Peter can do a whole job in half the time it takes Henry to do it. Together they can finish the job in 10 days. How many days will it take Peter to do the job alone?

Question 474870: Peter can do a whole job in half the time it takes Henry to do it. Together they can finish the job in 10 days. How many days will it take Peter to do the job alone?

Answer by karaoz(32) (Show Source): You can put this solution on YOUR website!

This is a nice problem.

Let p = the number of days required for Peter alone to do a whole job.
Let h = the number of days required for Henry alone to do a whole job.

There is one job and Peter can do 1/p parts of the job in one day.
Henry can do 1/h parts of the job in one day.
Together they can do 1/p + 1/h parts of the job in one day.
Together they can finish the job in 10 days, which means that 1/h + 1/p = 1/10.
This can be represented (after multiplying the equation by 10ph) as:
10p + 10h = ph.

The second equation comes from the first sentence: p = h/2.
Since we need only to find p it will be better to express h in terms of p.
From p = h/2, we have h = 2p.
Substitute this into
10p + 10h = ph, to get
10p + 20p = p(2p).
Solve for p:
30p = 2p²
Divide both sides of the equation by p (assuming p is not equal to 0) to get:
30 = 2p.

Finally,
p = 15 days.

Answer: It will take 15 days for Peter to do the job alone.

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