Question 136412: Please help me solve this word problem:
Garrett and Chris have a summer job washing cars at a car dealership. Chris can get the cars washed 3 hours quicker than Garrett can. Together, they can wash the cars in 5 hours. How long would it take Chris to do it alone? (Round your answer to the nearest tenth of an hour).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Chris can get the cars washed 3 hours quicker than Garrett can. Together, they can wash the cars in 5 hours. How long would it take Chris to do it alone? (Round your answer to the nearest tenth of an hour).
---------------------------------------
Chris DATA:
Time = x hrs/job ; Rate = 1/x job/hrs
--------------------
Garrett DATA:
Time = (x+3) hrs/job ; Rate = 1/(x+3) job/hrs
--------------------------------
Together DATA:
Time = 5 hrs/job ; Rate = 1/5 job/hr
=====================================
EQUATION:
rate + rate = tothether rate
1/x + 1/(x+3) = 1/5
5(x+3) + 5x = x(x+3)
10x+15 = x^2+3x
x^2-7x-15 = 0
x= [7 +- sqrt(49 -4*-15)]/2
x = [7 +- sqrt(109)]/2
-----------
This answer is irrational so time canonly be approximated:
x = 8.72.... hrs (Chris's time to do the job)
x+3 = 11.72... hrs (Garrett's time to do the job)
==================
Cheers,
Stan H.
|
|
|
