Work/Rate problem

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Thu Nov 02, 2017 10:56 am

An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes
OA is a

which formula will i use here to get the correct answer to this question? can any expert help me here?
Thank you

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Source: Beat The GMAT — Problem Solving | Thu Nov 02, 2017 10:56 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Thu Nov 02, 2017 3:42 pm

An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes
OA is a

which formula will i use here to get the correct answer to this question? can any expert help me here?
Thank you

Hi Roland2rule,
Let's take a look at your question.

The questions states that:
"The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes."

In one minute, the part of the tire made flat by the first puncture = 1/9
In one minute, the part of the tire made flat by the second puncture = 1/6

Now we can find out the part of the tire made flat by both the punctures in one minute by just adding them up.
In one minute, the part of the tire made flat by both the punctures =
$$=\frac{1}{9}+\frac{1}{6}$$
$$=\frac{2+3}{18}$$
$$=\frac{5}{18}$$

Reading it in reverse order, we can now say that both the punctures together will make the tire flat in 18/5 minutes.

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
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Our average student improves 98 points.

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by [email protected] » Fri Nov 03, 2017 1:48 pm

Hi Roland2rule,

This is an example of a "Work Formula" question - when you have two entities working together on a task, you can use the following formula to determine how long it will take the two entities to complete the task:

(A)(B)/(A+B) = time to complete the task (where A and B are the two times it takes the individuals to complete the task when working alone)

We're told that the first puncture would create a flat tire in 9 minutes and the second puncture would make a flat tire in 6 minutes. Plugging in those values, we'd have...

(9)(6)/(9+6) = 54/15 = 18/5 = 3 3/5 minutes to make a flat tire

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Thu Oct 31, 2019 5:17 pm

BTGmoderatorRO wrote:An automobile tire has two punctures. The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes. How long will it take for both punctures together to make the tire flat? (Assume the air leaks out at a constant rate.)

(A) 18/5 minutes
(B) 4 minutes
(C) 21/4 minutes
(D) 15/2 minutes
(E) 15 minutes
OA is a

which formula will i use here to get the correct answer to this question? can any expert help me here?
Thank you

The combined rate of the two punctures is:

1/9 + 1/6 = 2/18 + 3/18 = 5/18

Thus, the time to make a flat with both punctures is 1/(5/18) = 18/5 minutes.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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