If ‘A’ Can Complete a Task in 3 Hours and ‘B’ Can Complete the Same Task in 6 Hours GMAT Problem Solving

Question: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?

1. 1 hour
2. 1.5 hours
3. 2 hours
4. 2.5 hours
5. 4.5 hours

“If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Complete 2021”. 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.

Approach Solution 1:

There is only one approach to solve the problem statement.

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:
Given that a and b are the respective individual times needed for A and B workers (pumps, ...) to complete the job
Hence, the time needed for A and B working simultaneously to complete the job equals to T\(_A\)&\(_B\)= a*b/a+b hours, which is reciprocal of the sum of their respective rates (1/a +1/b = 1/t).
Also for rate problems it's good to know that:
TIME to complete one job=Reciprocal of rate.
For example:
6 hours needed to complete one job (time) --> 1/6 of the job done in 1 hour (rate).
Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.

Time*Rate=Distance
Time*Rate=Job

Now, as per the problem statement:

Given:

• ‘A’ can complete a task in 3 hours
• ‘B’ can complete the same task in 6 hours

Find out:

• How long will it take if both of them work together to complete the task?

A can complete task in 3 hours.

Hence, in 1 hour A can complete 1/3 of the work.

B can complete task in 6 hours.
Hence, in 1 hour B can complete 1/6 of the work.

Both together can complete how much work in 1 hour
= 1/3 + 1/6
= 3/6
= 1/2

So 1/2 work can be completed in 1 hour by A and B together.

Now we will calculate how much time it takes to complete the work by both A and B together.
= 2/1 hours
= 2 hours.

Correct Answer: C

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