Question

Two people working together can clean a pig pen in 4 hours. Working alone, it takes Thurman Mervin 3 hours longer to clear the pen than it would take Bobbi Sue. How long would it take Thurman Mervin to clean the mink farm alone? (Round answer to the nearest tenth.)

A. 6.4 hours

B. 7.8 hours

C. 9.4 hours

D. 10.2 hours

Answer 1

To find Thurman Mervin's cleaning time, we can set up an equation and solve for it based on the given information.

Step-by-step explanation:

To solve this problem, we can set up an equation based on the given information.

Let's say it takes Bobbi Sue x hours to clean the pig pen alone. Since Thurman Mervin takes 3 hours longer to clear the pen than it would take Bobbi Sue, it would take him (x + 3) hours.

When they work together, they can clean the pig pen in 4 hours, so their combined work rate is 1/4 of the job per hour. Bobbi Sue's work rate is 1/x of the job per hour, and Thurman Mervin's work rate is 1/(x + 3) of the job per hour.

Using the work rate formula, we can set up the equation:

1/x + 1/(x + 3) = 1/4

Now, we can solve this equation for x to find Bobbi Sue's cleaning time. Once we find x, we can substitute it into the expression (x + 3) to find Thurman Mervin's cleaning time.