Question 474870
<br> This is a nice problem.<br>
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.<br>
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.<br>
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 = 2p<sup>2</sup>
Divide both sides of the equation by p (assuming p is not equal to 0) to get:
30 = 2p.<br>
Finally,
p = 15 days.<br>
Answer: It will take 15 days for Peter to do the job alone.