Overview: We'll write 2 equations based upon the information given then use substitution to solve for Jen's time.

First, we'll assign variables:

P = time it takes for Pat to shelve

J = time it takes for Jen to shelve

The problem tells us that together they can shelve an entire cart in 24 min. We write this as...

P + J = 24

The problem also states that Pat can shelve 14 min faster than Jen. We write this as...

P = J - 14

We substitute the above equation for P in terms of J into the equation P + J = 24 and then solve for J...

(J -14) + J = 24

J - 14 + J = 24

J + J -14 = 24

2J = 38

J =19

(Jen can shelve an entire cart in 19 minutes by herself)

We can check our solution by solving for P and then making sure that P + J = 24

P = J -14

P = (19) -14

P = 5

5 + 19 = 24 The solution checks!

I hope that helps. Please ask if you have any questions or would like a clarification on any step.

-Steve

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