Question

During hurricane season, Bob and Jen fill sand bags every weekend. On Saturday, they both worked together 4 hours and filled 32 sand bags. Sunday, Jen was feeling rather stiff and only worked 2 hours compared to Bob's 6 hours. They filled 36 sand bags on Sunday. How many sand bags can Jen fill in 6 hours?

Answer 1

Let b=bob's rate of bags per hour; Let j=Jen's rate of bags per hour.

So b+J=32/4

So bob and Jen can fill 8 bags in one hour when working together.

Since bob works 6 hours and Jen works 2 hours, then bob's rate per hour times six hours and Jen's rate per hour times 2 hours equals 36 bags

6(b)+2(j)=36 bags

Rearranging the first equation, we get

b=8-j

Substituting in to the second equation, we get

6(8-j)+2j=36

48-6j+2j=36
48-4j=36
48-36=4j
12=4j
3=j

So 3 bags an hour is Jen's rate of filling bags of sand.

Since the question asks how many bags Jen can fill in six hours, we will multiply six times 3 and get

6(3)=18 bags