SOLUTION: Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 3 hours. How long does it take each of them working alone? Round your answers to th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 3 hours. How long does it take each of them working alone? Round your answers to th      Log On


   

Question 384139: Ron can mow the lawn in two hours more time than Paul. Working together they can mow the lawn in 3 hours. How long does it take each of them working alone? Round your answers to the nearest tenth of an hour, if necessary.
A)Paul: 4 hours, Ron: 8 hours
B)Paul: 5.2 hours, Ron: 7.2 hours
C)Paul: 7.2 hours, Ron: 5.2 hours
D)Paul: 8 hours, Ron: 4 hours
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

  Ron can mow the lawn in two hours more time than Paul       

Let x  and (x+2) represent Paul and Ron's times solo respectively

 Question states, per hour being the Equalizer

 1/x + 1/(x+2) = 1/3hr Multiplying each term by 3x(x+2) so as all denominators = 1

 3(x+2) + 3x = x(x+2)

 3x+ 6  + 3x = x^2 +2x

 x^2 - 4x - 6 = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

x+=+%284+%2B-+sqrt%28+40+%29%29%2F%282%29+

  x+=+%284+%2B-+2%2Asqrt%28+10+%29%29%2F%282%29+ 

x = -1.2  Or x = 5.2 (rounded to the nearest tenth)

tossing out negative solution

 x = 5.2hr, Pauls Time, Ron's 7.2hr