Question

!!!! Need help at least starting it off!!!
Pat and Jen volunteer at the library. Pat can shelve a full cart of books 14 minutes faster then Jen. If they work together, they can shelve a full cart in 24 min. How long does it take Jen to shelve a full cart by herself? ( helping me form a graph or someway to start will be extremely helpful.)

Answer 1

Let

P = time (in minutes) it takes for pat to do the job alone
J = time (in minutes) it takes for jen to do the job alone

we are told that " Pat can shelve a full cart of books 14 minutes faster then Jen", so that means Pat's time is 14 min less than Jen's time

ie

P = J - 14

Answer 2

For Pat, it takes P minutes to do the full job

That means he completes 1/P of the job in 1 minute

You can think of it this way

P minutes: 1 job

1 minute: 1/P job ... divided both parts of the ratio by P

Answer 3

So Pat's rate is 1/P of a job per minute

similarly, Jen's rate is 1/J of a job per minute

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combine the two rates

1/P + 1/J

J/(PJ) + P/(PJ)

( J + P )/(P*J)

this combined rate is equal to 1/24. You can see this with this ratio

1 job: 24 minutes (for both working together)

1/24 job: 1 minute (divide both parts by 24)

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So we have this equation

( J + P )/(P*J) = 1/24

cross multiplying gives you

24(J + P) = P*J

now plug in P = J - 14

24(J + J - 14) = (J - 14)*J

24(J + J - 14) = J(J - 14)

24(2J - 14) = J(J - 14)

48J - 336 = J^2 - 14J

I'll let you solve from here

Answer 4

Alright I will start on it now, thank you for the start.