Question

Bill and Tom decide to finish fixing their car. Bill can complete the given job in six hours, but Tom takes eight hours. They worked together for the first two hours, but then Bill went inside to watch the game. How long will it take Tom to finish their car?

Answer 1

Tom will take 2 hours and 50 minutes to finish the car.

Step-by-step explanation:

To find how long it will take Tom to finish the car, we need to calculate the work done by both Bill and Tom in the two hours they worked together. Bill can complete the job in 6 hours, so in 1 hour, he completes 1/6th of the job. Tom takes 8 hours to complete the job, so in 1 hour, he completes 1/8th of the job. In the 2 hours they worked together, together they completed 1/6 + 1/8 of the job. Simplifying this, we get 7/24.

To find how long it will take Tom to finish the remaining job, we subtract the work completed by both of them from the total job. Since 7/24th of the job is completed in 2 hours, the remaining job is 1 - 7/24 = 17/24 of the total job. Tom's rate is 1/8th of the job per hour, so to find how long it will take him to finish the remaining job, we divide 17/24 by 1/8. Simplifying this, we get 17/24 ÷ 1/8 = 17/24 x 8/1 = 68/24 = 2 and 20/24 hours. Converting this to a mixed number, we have 2 hours and 50 minutes. Therefore, it will take Tom 2 hours and 50 minutes to finish the car.