# Help with math puzzle

• Jul 4th 2014, 04:36 AM
burgess
Help with math puzzle
P and Q are engaged to a work. For P alone it takes more than 8 hours more to complete the job than if both worked together. If Q worked alone, he would need 4 and half hours more to complete the job than they both work together. What time would they take to do the work together?

Please tell me the procedure to solve the problem

Thanks
• Jul 4th 2014, 06:53 AM
HallsofIvy
Re: Help with math puzzle
When two people work together (or machines work, or hoses fill a tank, etc) their rates of work add. Let p be the rate of work of p in "job per hour" and let q be the rate of work of Q in "job per hour". Together they work at the rate of p+ q "job per hour".

Quote:

For P alone it takes more than 8 hours more to complete the job than if both worked together
Surely that's not right. If all we know is that it take P "more than 8 hours more" we have no idea how long it would actually take. You must mean
Quote:

For P alone it takes 8 hours more to complete the job than if both worked together
A rate p "job per hour" it would take P 1/p hours to complete the job. At p+ q, working together, it would take 1/(p+ q) hours.
1/p= 1/(p+ q)+ 8.

Quote:

If Q worked alone, he would need 4 and half hours more to complete the job than they both work together.
At rate q "job per hour" it would take Q 1/q hours to complete the job.
1/q= 1/(p+ q)+ 4.

Solve those two equations for p and q and then find 1/(p+ q).