Question

John and his little brother Kevin have a job that requires them to rake and bag leaves at a large

house in their neighborhood. Suppose it takes John 2 hours to do the job alone and Kevin 3 hours to do the job alone. At these rates, how long will it take both boys to complete the job together?

Answer 1

To determine how long it will take both John and Kevin to complete the job together, we can use the concept of "work rates."

Let's start by calculating their individual work rates. John takes 2 hours to complete the job alone, so his work rate is 1/2 of the job per hour (1 job / 2 hours = 1/2 job per hour). Similarly, Kevin takes 3 hours to complete the job alone, so his work rate is 1/3 of the job per hour (1 job / 3 hours = 1/3 job per hour).

When they work together, their work rates add up. So, to find the time it takes for them to complete the job together, we can add their work rates and then calculate the reciprocal of the sum.

John's work rate: 1/2 job per hour

Kevin's work rate: 1/3 job per hour

Their combined work rate: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 job per hour

To find the time it takes for them to complete the job together, we need to calculate the reciprocal of their combined work rate:

Time = 1 / combined work rate

Time = 1 / (5/6) = 6/5 hours

So it will take both John and Kevin 6/5 hours or 1 hour and 12 minutes to complete the job together.