BTGmoderatorLU wrote:Source: Manhattan Prep

Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of \(m\) dollars when the work is completed. If Angela decides to pay Linda \(n\) dollars so that they would have received the same compensation per hour worked, what is \(n\) in terms of \(m\)?

A. \(\frac{1}{2}m\)
B. \(\frac{1}{3}m\)
C. \(\frac{1}{4}m\)
D. \(\frac{1}{5}m\)
E. \(\frac{1}{6}m\)

The OA is D

Say Angela working alone takes 1 hour to pain; thus, Linda takes 3/2 hours to paint the same house.

Thus, for 1 + 1.5 = 2.5 hours they got $2m. The per-hour rate = 2m/2.5 = 4m/5 dollar per hour

Since Angela worked for 1 hour, she should get (4m/5)*1 = 4m/5 dollars

Since Angela got $m, should give Linda m - 4m/5 = m/5 dollars

The correct answer: D

Hope this helps!

-Jay
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