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# Machines M1 andM2 purify air at different constant rates. Machine M1 ,

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Machines M1 andM2 purify air at different constant rates. Machine M1 , [#permalink]

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03 Feb 2018, 02:28
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Difficulty:

75% (hard)

Question Stats:

55% (01:48) correct 45% (02:02) wrong based on 64 sessions

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Machines M1 and M2 purify air at different constant rates. Machine M1, operating alone for 5 hours, purified the air within part of one floor of a building; then Machine M2 , operating alone for 4 hours, purified the air within the rest of the floor. How many hours would it have taken Machine M1 operating alone to purify the air in the entire floor?

(1) M2 purified one cubic foot of air per minute within the 9 rooms on the floor it purified.

(2) M1 purified fifty percent more air in 5 hours than M2 purified in 4 hours

Source: Gmatfree

Please explain how to express the two statements in equations.

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Re: Machines M1 andM2 purify air at different constant rates. Machine M1 , [#permalink]

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03 Feb 2018, 04:02
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TaN1213 wrote:
Machines M1 and M2 purify air at different constant rates. Machine M1, operating alone for 5 hours, purified the air within part of one floor of a building; then Machine M2 , operating alone for 4 hours, purified the air within the rest of the floor. How many hours would it have taken Machine M1 operating alone to purify the air in the entire floor?

(1) M2 purified one cubic foot of air per minute within the 9 rooms on the floor it purified.

(2) M1 purified fifty percent more air in 5 hours than M2 purified in 4 hours

Source: Gmatfree

Please explain how to express the two statements in equations.

to find total operating hours for M1 to purify entire floor alone, we need the values of rate of M1 and the amount of air

Statement 1: Nothing mentioned about M1 or there is no relation given to connect M2 & M1. Insufficient

Statement 2: M2 purifies the remaining air in 4 hours. M1 did 1.5 times the work done by M2 in 5 hours. Hence M1 would have taken $$\frac{5}{1.5}$$ to purify the remaining air

Therefore total time taken $$= 5+\frac{5}{1.5}$$ hours. Sufficient

Option B

Alternatively to visualize statement 2, let M1 did y work in 5 hours and M2 did x work in 4 hours

this implies y=1.5x =>x=y/1.5

so M1 has to complete x work. M1 does y work in 5 hours

hence y/1.5 work will be completed in = (5/y)*(y/1.5)=5/1.5

therefore total time taken by M1 = 5+5/1.5
Re: Machines M1 andM2 purify air at different constant rates. Machine M1 ,   [#permalink] 03 Feb 2018, 04:02
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