SOLUTION: Andy and Violet are planting trees. Andy can plant a tree 1.25 times as quickly as Violet can. When they work together, they can plant 25 trees in an hour and 10 minutes. How long

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Andy and Violet are planting trees. Andy can plant a tree 1.25 times as quickly as Violet can. When they work together, they can plant 25 trees in an hour and 10 minutes. How long       Log On


   

Question 924418: Andy and Violet are planting trees. Andy can plant a tree 1.25 times as quickly as Violet can. When they work together, they can plant 25 trees in an hour and 10 minutes. How long would it take Violet to plant the 25 trees if she were working alone?
Found 2 solutions by ankor@dixie-net.com, ptaylor:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Andy and Violet are planting trees.
Andy can plant a tree 1.25 times as quickly as Violet can.
When they work together, they can plant 25 trees in an hour and 10 minutes.
How long would it take Violet to plant the 25 trees if she were working alone?
:
Change 1 hr 10 min to 1.167 hrs
:
let t = time required by A to plant 25 trees
then
1.25t = time required by V to plant 25 trees
:
let the completed job = 1 (the planting of 25 trees)
:
A shared work equation
1.167%2Ft + 1.167%2F%281.25t%29 = 1
multiply equation by 5t, get rid of the denominators
5(1.167) + 4(1.167) = 5t
5.835 + 4.668 = 5t
10.5 = 5t
t = 10.5/5
t = 2.1 hrs A working alone
then
1.25 * 2.1 = 2.625 hrs V working alone, that's 2 hr + .625(60) = 2 hrs 37.5 min
:
:
See if that checks out
1.167%2F2.1 + 1.167%2F%282.625%29 ~ 1

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=time it takes Violet to plant 25 trees working alone
Then Violet works at the rate of 25/x trees per hour
1.25x=time it takes Andy to plant 25 trees
Then Andy works at the rate of 25/(1.25x)=25/((5/4)x)=25*(4/5x)=100/5x trees per hour
Together they can plant 25 trees in an 1 1/6 or 7/6 of an hour
Together they work at the rate of 25/(7/6) or 150/7 trees per hour
So our equation to solve is:
25/x + 100/5x=150/7 multiply each term by 35x
875+700=750x
750x=1575
x=2.1 hours ---time it takes Violet to plant 25 trees
1.25x=1.25*2.1=2.625---time it takes Andy to plant 25 trees
CK
In 1hr 10min=7/6 hr, Violet can plant (25/2.1)*(7/6)=175/12.6=13.9 trees
In 1hr 10min=7/6 hr, Andy can plant (25/2.625)(7/6)=175/15.75=11.1 trees
13.9+11.1=25 trees :)
Hope this helps---ptaylor