John takes 3 hours longer than andrew to peel 400 pounds of

John takes 3 hours longer than andrew to peel 400 pounds of apples. if together they can peel 400 pounds of apples in 9 hours, then how long would it take john to peal the apples working alone?

Solution

Andrew Data:
time to do job = \"x\" hrs.
rate doing job = 1/x job/hr.
John Data:
time to do job = \"x+3\" hrs.
rate doing job = 1/(x+3) job/hr.
Together Data:
time to do job = 9 hrs.
rate doing job = 1/9 job/hr.
EQUATION:
Rate + Rate = Rate
1/x + 1/(x+3) = 1/9
9(x+3)+9x=x(x+3)
18x+27=x^2+3x
x^2-15x-27=0
Use quadratic formula to get:
x=[15+sqrt(333)]/2 or [15-sqrt(333)]/2
x=16.624 hrs.
The 2nd value of \"x\" is negative.
John\'s time = x+3 = 19.624 hrs.