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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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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

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

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

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New post 17 Sep 2019, 03:34
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


Official Explanation



We have a combined rate question here. The rates involve air purified per hour, but we aren't given any quantities or measures of air in the prompt, just "parts" of the floor, so we cannot calculate a rate for either machine yet. On to the statements, separately first.

Statement (1) gives us the rate of one of the machines. But we don't know the rate of the first machine. So we can imagine two cases, one in which the first machine is much slower than the second, and another in which the first machine is much faster than the second. In those two cases, we'll get quite different results for how long it would take the first machine to do it all alone. So Statement (1) is insufficient.

In the second statement, we get a comparative measure of the amounts of air these things purified. If M2 purified x amount of air in 4 hours, then Statement (2) is telling us that

air/hours = x/4 = 1.5x/5

It also means that the total air on the floor is 2.5x, since the combined efforts of the two machines covered the whole floor. Working with the rate for M1, we have

1.5x/5 = 2.5x/(25/3) = (total air)/hours

To double-check that we're right, we can do the same calculation for M2:

x/4 = 2.5x/10 = (total air)/hours

It checks out that it would take less time for M1 --namely, 25/3 or 8 1/3 hours--to do the whole floor than M2, since M1 is faster. Statement (2) is sufficient.

The correct answer is (B).
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Re: Machines M1 andM2 purify air at different constant rates. Machine M1 ,  [#permalink]

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New post 17 Sep 2019, 03:35
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


Video Explanation




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Re: Machines M1 andM2 purify air at different constant rates. Machine M1 ,   [#permalink] 17 Sep 2019, 03:35
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