An Automobile Tire has Two Punctures GMAT Problem Solving

Question: 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.)

  1. 18/5 minutes
  2. 4 minutes
  3. 21/4 minutes
  4. 15/2 minutes
  5. 15 minutes

Correct Answer: A

Solution and Explanation:
Approach Solution 1:

It is asked How long will it take for both punctures together to make the tire flat?
The first puncture flattens the tyre in 9 minutes.
1 m = 1/9 of a tyre.
It takes six minutes to flatten a second punctured tyre.
1 m = 1/6 of a tyre.
Adding both tyres we get
1 minute is = \(\frac{1}{9}\)+ \(\frac{1}{6}\)= \(\frac{5}{18}\)of a tyre.
Therefore
Time required to flatten a tyre:
1 minute = \(\frac{5}{18}\)of the tyre
\(\frac{1}{5}\)minute = \(\frac{1}{18}\)of the tyre
18/18 of the tyre = 1/5 x 18
= \(\frac{18}{5}\)min
The tyre can be flattened down in \(\frac{18}{5}\)minutes.

Approach Solution 2: 
There is another approach to this question which is fairly simple
This seems to be a sample of a "Work Formula" question.
Using the formula below, you may estimate how long it will take two entities to finish a task when they are working together.
so,
Time to complete the task is = (A)(B)/(A+B), where A and B are the two times that each person needs to finish the assignment when working alone.
According to the information provided, the first puncture would result in a flat tyre in 9 minutes and the second would do so in 6 minutes. With those values entered, we'd have…
\(\frac{(9)(6)}{(9+6)}\)
= \(\frac{54}{15}\)
= \(\frac{18}{5}\)

Approach Solution 3:

One releases air in 9 min ; so in 1 min, it will release 1/9
other releases in 6 minutes ; so in 1 min it will release 1/6
so in 1 minute combined they will release 1/9+1/6= 15/54...
so entire air will be released in 54/15=18/5

“An automobile tire has two punctures.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


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