SOLUTION: Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 of the job, how long would Jeff need
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 of the job, how long would Jeff need
Log On
Question 400107: Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 of the job, how long would Jeff need to do the job alone? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Mutt and Jeff need to paint a fence. Mutt can do the job alone 2 hours faster than Jeff. If together they work for 34 hours and finish only 2/3 the job, how long would Jeff need to do the job alone?
-----
Mutt DATA:
time = x hr/job ; rate = 1/x job/hr
---
Jeff DATA:
time = x+2 hr/job ; rate = 1/(x+2) job/hr
----
-------
Together DATA:
time = 34 hr/(2/3)job = 51 hr/job : rate = 1/51 job/hr
======
Equation:
rate + rate = together rate
1/x + 1/(x+2) = 1/51
51(x+2) + 51x = x(x+2)
102x+102 = x^2+2x
===
x^2 - 100x - 102 = 0
-----
I graphed this; x is very close to 102 hr (Mutt's time to do job alone)
Jeff's time to do the job alone is x+2 = 104 hrs
(