Work Problem

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PGMAT: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Fri Jul 23, 2010 1:30 pm

by PGMAT » Sat Jan 29, 2011 2:15 pm

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?

1/2m
1/3m
1/4m
1/5m
1/6m

Can some help me solve this algebraically?

Thanks

D

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Source: Beat The GMAT — Problem Solving | Sat Jan 29, 2011 2:15 pm

Everest: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jan 03, 2011 4:56 pmFollowed by: 1 member; Location: Calif; Thanked: 2 times

by Everest » Sat Jan 29, 2011 3:16 pm

suppose Angela spends 1 hr and linda spends 1.5 hrs

Therefore they receive 2m dollars for working 2.5 hrs

=> for 2.5 hrs they received 2m dollars then for 1 hr they need to receive 4/5 *m dollars

Angela should receive 4/5 *m dollars

Linda should receive 3/2 * 4/5 * m dollars => 6/5 m dollars

Since angela decides to pay linda n dollars => n = 6/5 * m dollars

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Jan 29, 2011 3:18 pm

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?

TIME --> A=1.5L
PAYMENT --> M

(M-N)/A = (M+N)/L, FIND N IN TERMS OF M?
(M-N)*L=(M+N)*A --> (M-N)*1.5=(M+N)*1 --> 1.5M-1.5N=M+N --> 0.5M=2.5N --> N=0.5M/2.5 --> M/5

answer D, 1/5 * m

sorry for the first glitch ...

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Everest: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jan 03, 2011 4:56 pmFollowed by: 1 member; Location: Calif; Thanked: 2 times

by Everest » Sat Jan 29, 2011 3:27 pm

Night reader wrote: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?

TIME --> A=1.5L
PAYMENT --> M

(M-N)/A = (M+N)/L, FIND N IN TERMS OF M?
(M-N)*L=(M+N)*A --> (M-N)*1.5=(M+N)*1 --> 1.5M-1.5N=M+N --> 0.5M=2.5N --> N=0.5M/2.5 --> M/5

answer D, 1/5 * m

sorry for the first glitch ...

how lind will receive 1/5 * m dollars by working 50% more time than angela?

=> angela will receive 2m - 1/5 *m dollars => 9/5 * m dollars by working less time. can you justify?

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Jan 29, 2011 3:35 pm

Everest wrote:
Night reader wrote: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?

TIME --> A=1.5L
PAYMENT --> M

(M-N)/A = (M+N)/L, FIND N IN TERMS OF M?
(M-N)*L=(M+N)*A --> (M-N)*1.5=(M+N)*1 --> 1.5M-1.5N=M+N --> 0.5M=2.5N --> N=0.5M/2.5 --> M/5

answer D, 1/5 * m

sorry for the first glitch ...

how lind will receive 1/5 * m dollars by working 50% more time than angela?

=> angela will receive 2m - 1/5 *m dollars => 9/5 * m dollars by working less time. can you justify?

Angela will receive m-1/5 *m dollars OR 4m/5 dollars
Linda will receive m+1/5 *m dollars OR 6m/5 dollars

you found how much will Linda receive, but the question requires to find n in terms of m.

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Everest: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Mon Jan 03, 2011 4:56 pmFollowed by: 1 member; Location: Calif; Thanked: 2 times

by Everest » Sat Jan 29, 2011 3:44 pm

True, got it....

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PGMAT: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Fri Jul 23, 2010 1:30 pm

by PGMAT » Sat Jan 29, 2011 4:27 pm

Night reader wrote: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?

TIME --> A=1.5L
PAYMENT --> M

(M-N)/A = (M+N)/L, FIND N IN TERMS OF M?
(M-N)*L=(M+N)*A --> (M-N)*1.5=(M+N)*1 --> 1.5M-1.5N=M+N --> 0.5M=2.5N --> N=0.5M/2.5 --> M/5

answer D, 1/5 * m

sorry for the first glitch ...

nice.... thank you.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 30, 2011 3:14 am

PGMAT wrote: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?

1/2m
1/3m
1/4m
1/5m
1/6m

Can some help me solve this algebraically?

Thanks

D

I would plug in values for the hourly rate and for the time worked.

Let hourly rate = $2 per hour.
Let time for Angela = 2 hours.
Since Linda works 50% longer, time for Linda = (1.5)*2 = 3 hours.
Total pay = (rate) * (total time) = 2*(2+3) = $10.
Since each received m dollars in advance, m = 10/2 = $5.
Since Angela should earn 2*2 = $4, she must give Linda n = 5-4 = $1.

The question asks for the value of n=1. Now we plug m=5 into all the answer choices to see which yields our target of 1.

Only answer choice D works:
(1/5)*m = 1/5 * 5 = 1.

The correct answer is D.

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