SOLUTION: 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 togeth

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?
--------------------------
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?"
----------------
The time working together is (using a math shortcut)
45*18/(45+18)
= 90/7 minutes, or apx 12.86 minutes.

RELATED QUESTIONS
Andrea can ride her bike 2 mph faster than Ruby. It takes andrea 48 minutes less to... (answered by mananth)
John can rake his yard in 40 minutes, his brother Bob can rake the yard in one hour, how... (answered by stanbon)
Andrea has an average of 87% on her first 5 tests. She has one test left to take. What is (answered by checkley77)
Andrea ran and biked for a total of 32 miles in 4 hours. Her average running speed was 5... (answered by Boreal)
Andrea and Stacy both leave the coffee shop at the same time, but in opposite directions. (answered by solver91311)
Andrea is 5 years older than Kristina. In 3 years the sum of their ages will be 45. How... (answered by josgarithmetic)
"A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the... (answered by josgarithmetic)
Andrea can rollerblade faster than most skateboards, she can go 250 feet in 10 seconds.... (answered by TimothyLamb)
Martha can rake leaves in her yard in 8 hours. Her brother can rake leaves in 4 hours.... (answered by Cromlix)