Question 415776: It takes Troy 3 hours to mow his family's large lawn. With his little brother's help, he can finish the job in only 2 hours. How long would it take the little brother to mow the entire lawn?
A) 4 hrs B) 5 hrs C) 5.5 hrs D) 6 hrs E)6.75 hrs
Found 2 solutions by ewatrrr, htmentor:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
Let x represent time for his little brother to mow the entire lawn 'solo'
Question states*** Per hour being the Equalizer
1/3 + 1/x = 1/2
Solving for x
2x + 6 = 3x |multiplying thru by 6x so as all denominators = 1
x = 6hr, the time for his little brother to mow the entire lawn 'solo'
CHECKING our Answer***
1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
Answer by htmentor(1343)  (Show Source):
You can put this solution on YOUR website! Let A = the area of the lawn
Troy's mowing rate R = (Lawn Area)/Total Time) = A/3
With brother's help, he covers the area of the lawn A in 2 hours
We need to determine his brother's mowing rate, r.
We know that 2*(R + r) = A, since they both spend 2 hours, mowing at their own rates, to cover the lawn area A.
And since R = A/3, we have 2*(A/3 + r) = A
Solving for r -> r = A/2 - A/3, or r = (3A - 2A)/6 -> r = A/6
Therefore, it would take Troy's brother 6 hours to cover the lawn area, A
Ans = (D)
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