SOLUTION: A & B working together can do a job for 10 days.If each works alone A takes 5 days longer than B to do the job.How long will it take each one of them to do the job.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A & B working together can do a job for 10 days.If each works alone A takes 5 days longer than B to do the job.How long will it take each one of them to do the job.       Log On


   

Question 135923: A & B working together can do a job for 10 days.If each works alone A takes 5 days longer than B to do the job.How long will it take each one of them to do the job.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let x= amount of time in days that it takes B to do the job working alone
B, then, works at the rate of 1/x of the job per day
x+5=amount of time in days that it takes A working alone
A, then, works at the rate of 1/(x+5) of the job per day
Together A&B works at the rate of 1/x + 1/(x+5)=(x+5+x)/x(x+5)=
(2x+5)/x(x+5) of the job per day, we are told that, working together, it takes them 10 days so our equation to solve is
((2x+5)/x(x+5))*10=1 (1 job, that is) multiply each term by x(x+5)
10(2x+5)=x(x+5)
20x+50=x^2+5x subtract 20x and 50 from each side
x^2-15x-50=0 quadratic in standard form; solve using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%2815+%2B-+sqrt%28+225%2B200+%29%29%2F%282%29+
x+=+%2815+%2B-+20.616%29%2F%282%29+
x+=+%2815+%2B20.616%29%2F%282%29+
x+=+17.808 days ---------------------amount of time needed by B working alone
17.808+5=22.808----------------------------amount of time needed by A working alone
FORGET THE NEGATIVE VALUE FOR x, TIME WOULD BE POSITIVE IN THIS CASE
CK
(1/17.808)+(1/22.808)=1/10
0.05615+0.0438=0.1
0.099999~~~~~~0.1
Hope this helps ------ptaylor