Question

Frank can do a job in 6 hours. Mike can do it in 4 hours. How long will it take them to complete the job together?

A) 2 hours
B) 3 hours
C) 4 hours
D) 2.4 hours

Answer 1

Frank and Mike will take 2.4 hours to complete the job together when they work at their combined rate, which is the sum of their individual rates of work.

Step-by-step explanation:

To find out how long it will take Frank and Mike to complete the job together, we need to add their rates of work. Frank can complete the job in 6 hours, which means he can do 1/6 of the job in one hour. Mike can complete it in 4 hours, so he can do 1/4 of the job in one hour. When working together, we add their rates of work to find the combined rate.

Frank's rate: 1/6 of the job per hour
Mike's rate: 1/4 of the job per hour
Combined rate: (1/6 + 1/4) of the job per hour

To add fractions, we find a common denominator:

Combined rate: (1/6 + 1/4) = (2/12 + 3/12) = 5/12 of the job per hour

Now to find out how long it will take them to complete the job together, we divide the whole job (1) by their combined rate:

Time taken together: 1 / (5/12) = (1 * 12/5) = 12/5 hours = 2.4 hours

Therefore, Frank and Mike will take 2.4 hours to complete the job together, so the correct answer is D) 2.4 hours.