Question: One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill \(\frac{2}{3}\)of the tank?

1. \(\frac{8}{15}\)hr
2. \(\frac{3}{4}\)hr
3. \(\frac{5}{4}\)hr
4. \(\frac{15}{8}\)hr
5. \(\frac{8}{3}\)hr

Answer:
Solution with Expalnation:
Approach Solution (1):

Rate of the first pipe is \(\frac{1}{5}\)tank/hour

Rate of the second pipe is \(\frac{1}{3}\)tank/hour

Their combined rate is \(\frac{1}{5}\)+ \(\frac{1}{3}\)= \(\frac{8}{15}\)tank/hour

Both pipes working together to fill \(\frac{2}{3}\)of the tank will take (time) = \(\frac{work}{rate}=(\frac{2}{3})(\frac{8}{15})=(\frac{2}{3})*(\frac{15}{8})=\frac{5}{4}hours\)

Correct Option: C

Approach Solution (2):

Work = \(\frac{(A)(B)}{(A+B)}\)where A and B are the individual times to complete the task
The two pipes can fill the tank in 5 hours and 3 hours, respectively. Working together, it would \(\frac{(5)(3)}{(5+3)}=\frac{15}{8}\)take hours to fill the entire tank
We are asked how long it would take to fill \(\frac{2}{3}\)of the tank, so we have to multiply the above number by \(\frac{2}{3}\)

\(\frac{2}{3}*\frac{15}{8}=\frac{30}{24}=\frac{5}{4}\)hours

Correct Option: C

Approach Solution (3):

The combined rate of the pipes is \(\frac{1}{5}+\frac{1}{3}=\frac{3}{15}+\frac{5}{15}=\frac{8}{15}\)

If we let n = the time it takes to fill \(\frac{2}{3}\)of the tank, then:

\((\frac{8}{15})n=\frac{2}{3}\)

Multiply by 15, we have:
8n = 10
n = \(\frac{10}{8}=\frac{5}{4}hours\)

Correct Option: C

“One inlet pipe fills an empty tank in 5 hours. A second inlet GMAT Problem Solving

Question: One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill \(\frac{2}{3}\)of the tank?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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