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Question 191642: Andrea can rake her Dad's yard in 45 minutes. Andrea's brother Bradford rakes one and one-half times faster than Andrea. How long would it take them to rake their Dad's yard together?
Found 3 solutions by ptaylor, nerdybill, Alan3354:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes them to rake their dad's yard together
So, together they rake the yard at the rate of 1/x yard per min
Andrea rakes the yard at the rate of 1/45 yard per min
Then Bradford rakes at the rate of (1.5)*(1/45)=(3/2)(1/45)=3/90=1/30 yard per min
Now our equation to solve is
1/45 +1/30 = 1/x multiply each term by 180x
4x+6x=180 collect like terms
10x=180
x=18 min-------------------amount of time it takes them to rake their dad's yard together
CK
In 18 min Andrea can do (1/45)*18=18/45=2/5 of the lawn
In 18 min, Bradford can do (1/30)*18=18/30=3/5 of the lawn
2/5 +3/5 =5/5 (the whole lawn)
Hope this helps---ptaylor
Answer by nerdybill(7384)  (Show Source):
You can put this solution on YOUR website! Andrea can rake her Dad's yard in 45 minutes. Andrea's brother Bradford rakes one and one-half times faster than Andrea. How long would it take them to rake their Dad's yard together?
.
Andrea's rate:
1 job per 45 minutes
.
Brother's rate:
1.5x = 45
x = 45/1.5
x = 1 job per 30 minutes
.
Let t = time (in hours) it would take for them to work together
then
(1/45)t + (1/30)t = 1
30t + 45t = 1350
75t = 1350
t = 1350/75
t = 18 minutes
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Andrea can rake her Dad's yard in 45 minutes. Andrea's brother Bradford rakes one and one-half times faster than Andrea. How long would it take them to rake their Dad's yard together?
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1.5 times faster is 2.5 times as fast, not 1.5 times as fast.
So Bradford can rake the yard in 45/2.5 minutes, or 18 minutes, alone.
Right? If not, is "1 times faster" the same speed? If it's the same speed, then why say "faster?"
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The time working together is (using a math shortcut)
45*18/(45+18)
= 90/7 minutes, or apx 12.86 minutes.
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