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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