Shawna can sweepa porch in 8 minutes

Question

shawna can sweep a porch in 8 minutes, when her friend Jennifer helps out, it takes 4.95 minutes, how long would it take for Jennifer to sweep the porch by her self? (Please explain in detail as if you were teaching)

Answer 1

Shawna sweep a porch in 8 minutes, that means in 1 minute, she only can finish 1/8. 

 

when Jennifer help her, they take 4.95 minutes, that is, Shawna finish 1/8*4.95 = 4.95/8 =0.61875

 

So the left part must be finished by Jennifer, that is 1-0.61875=0.38125

 

Jennifer finish these part also takes 4.95 minutes, so in 1 minute, she will finish 0.38125/4.95=0.077

 

so the total time Jennifer can finish a porch is 1/0.077=13 minutes.

 

Answer 2

William, the more traditional way to solve this problem is close to what Chunli showed you. We are going to look at how much is done in one minute. We'll call Jennifer's time j.

 

So, in one minute, Shawna gets 1/8 of the job done. In one minute, Jennifer gets 1/j of the job done. Together, they get 1/4.95 of the job done in one minute.

 

1/8 + 1/j = 1/4.95

 

Now we need a common denominator. 8(j)(4.95) = 39.6j

 

4.95j/39.6j + 39.6/39.6j = 8j/39.6

 

With the denominators all the same, we can deal with ONLY the numerators.

 

4.95j + 39.6 = 8j

            3.05j = 39.6

                    j = 13

 

As Chunli said, Jennifer's time by herself is 13 minutes.

 

Let's check...

 

1/8 + 1/13 = 1/4.95

64.4/514.8 + 39.6/514.8 = 104/514.8

64.4 + 39.6 = 104

104 = 104

 

Boom.