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
(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
P + J = 24
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.
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