SOLUTION: A landscaping crew is using three different lawnmowers to cut a large lawn. Lawnmower A can cut the entire lawn by itself in 4 hours. Lawnmower B is 3 times as fast as Lawnmower C.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A landscaping crew is using three different lawnmowers to cut a large lawn. Lawnmower A can cut the entire lawn by itself in 4 hours. Lawnmower B is 3 times as fast as Lawnmower C.      Log On


   

Question 985523: A landscaping crew is using three different lawnmowers to cut a large lawn. Lawnmower A can cut the entire lawn by itself in 4 hours. Lawnmower B is 3 times as fast as Lawnmower C. If all three mowers are used to cut the grass, the entire job will only take 2 hours. How fast can Lawnmower B cut the grass?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A landscaping crew is using three different lawnmowers to cut a large lawn.
Lawnmower A can cut the entire lawn by itself in 4 hours.
Lawnmower B is 3 times as fast as Lawnmower C.
If all three mowers are used to cut the grass, the entire job will only take 2 hours.
How fast can Lawnmower B cut the grass?
:
let b = time required by mower b
"mower B is 3 times as fast as Lawnmower C" therefore
3b = time required by mower c
let the completed job = 1, each will do a fraction of the job, the 3 fractions add up to 1
:
A shared work equation
2%2F4 + 2%2Fb + 2%2F%283b%29 = 1
reduce the 1st fraction
1%2F2 + 2%2Fb + 2%2F%283b%29 = 1
Multiply equation by 6b, cancel the denominators and you have
3b(1) + 6(2) + 2(2) = 6b
3b + 12 + 4 = 6b
16 = 6b - 3b
16 = 3b
b = 16/3
b = 51%2F3 hrs time for B mower alone
:
:
Confirm this on your calc (c takes 3(5.333) which is 16 hrs)
2%2F4 + 2%2F5.333 + 2%2F16 = 1
.5 + .375 + .125 = 1