4.3k views
5 votes
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

User Eawenden
by
7.8k points

1 Answer

2 votes
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.
User SOS
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories