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Question 156074: Stan and Hilda can mow the lawn in 30 min if they work together. If Hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone?
What I tried:
Since it took 30 min for both to mow the lawn, I figured it would take stan to do 1/2 the lawn in 20 min, and hilda 10 min. so it would take stan 40 min to do the lawn alone. but nope, wrong answer :(
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! AT LEAST YOU WERE CLOSE!!!
Let x=amount of time it takes Stan to mow the lawn alone
Then Stan mows at the rate of 1/x lawn per min
Let y=amount of time it takes Hilda to mow the lawn alone
Then Hilda mows at the rate of 1/y lawn per min
Together, Stan and Hilda mows the lawn at the rate of 1/x + 1/y lawn per min and we are basically told that this equals 1/30 lawn per min
So:
1/x+1/y=1/30 multiply each term by 30xy
30y+30x=xy------------------------------------eq1
Now we are also told that Hilda works twice as fast as Stan, so:
y=x/2 or
x=2y-----------------------------------eq2
Substitute x=2y from eq2 into eq1:
30y+30(2y)=(2y)*y simplify
30y+60y=2y^2 or
2y^2=90y divide each side by 2
y^2=45y subtract 45y from each side
y^2-45y=0 Quadratic in standard form with c=0 and it can be factored:
y(y-45)=0
y=0----------------------------not a solution
and
y=45 min----------------amount of time it takes Hilda working alone
From eq2, x=2y; x=2*45=90 min----------------amount of time it takes Stan working alone
CK
1/45 + 1/90=1/30
2/90 + 1/90=1/30
3/90= 1/30
1/30= 1/30
Hope this helps---ptaylor
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