Question

Jeff takes 5 hour longer to build a fence than it takes bill. when they work together, it takes them 6 hours. how long would it take bill to do the job alone

Answer 1

Best Answer: Bill's time to do the whole job, B
Jeff's time, B + 5
time they actually work, 6.

6/B + 6/(B+5) = 1
6(B+5) + 6B = B(B+5)
6B + 30 + 6B = B² + 5B
B² - 7B - 30 = 0
(B - 10)(B + 3) = 0
B = 10 or B = -3, and we reject the negative solution.

the equation is based on adding the fractions of the whole job each does. if Bill takes B hours to do the whole thing and works 6, he does 6/B of the job. similarly for Jeff.

in the 2nd problem,
a = time of experienced accountant
2a = time of new accountant
10 = time each actually works

10/a + 10/(2a) = 1 ........ multiply all by a
10 + 5 = a
a = 15 hr.