Question

Kara starts tying a baby quilt at the local community center. Each quilt takes 200 ties to complete. Ten minutes later Julie joins Kara, and both stay to finish the quilt. Kara ties 6 per minute and Julie can tie 11 per minute.a. Write an expression to show the number of ties Kara has completed after minutes.b. Using the same variable , write an expression for the number of ties Julie has completed.c. If you know they finished the quilt, write an equation to model the situation.d. How many minutes did it take them to finish the quilt?e. How many did each of them tie?f. Suppose they tied the same amount. How long would it take?g. How many did each of them tie?

Answer 1

a)
`K(t)=6(tie)/(min)(t)`

b)
`J(t)=11(tie)/(min)(t)`

c)
`T_(f)(t)=K(t+10)+J(t)` where
`T_(f)(t)`= number ties finished per unit time

d) t≅8.24min

e) K=109tie

J=91tie

f) K≅16.6min

J≅9.09min

Explanation:

Data

`Kara_((K))=6(tie)/(min)\\Julie(J)=11(tie)/(min)`

Kara begins ten minutes before julie, so when julie joins kara she has 60 ties

t=10
`k=6(tie)/(min)*10min=60tie`

a)
`K(t)=6(tie)/(min)(t)`

b)
`J(t)=11(tie)/(min)(t)`

c)
`T_(f)(t)=K(t+10)+J(t)` where
`T_(f)(t)`= number ties finished per unit time

d) if kara already has 60 ties and makes 6 per minute and Julie makes 11 per minute then per minute they makes 17 ties, so one minute per 17 ties for 200 ties ¿how long?.
`t=((200-60)tie*min)/(17tie)`≅8.24min

e) K=60tie+6tie/min*8.24min=109tie

J=11tie/min*8.24min=91tie

f) K=100tie*min/6tie≅16.6min

J=100tie*min/11tie≅9.09min

Note: the amount of ties were rounded to the nearest decimal