Question

Jack and Walter work in a store's gift-wrapping department. Jack can wrap 28 boxes in 2 hours, while Walter takes 3 hours to wrap 36 boxes of the same size. One day they work together for t hours to gift wrap 65 boxes. Which equation models this situation?

Answer 1

"Jack can wrap 28 boxes in 2 hours"
Jack wraps 28 boxes/(2 hours) = 14 boxes/hour

"Walter takes 3 hours to wrap 36 boxes"
Walter wraps 36 boxes/(3 hours) = 12 boxes/hour

Together they wrap 14+12 = 26 boxes per hour.
t hours × 26 boxes/hour = 65 boxes

Answer 2

Answer: They work for 2.5 hours to gift wrap 65 boxes.

Explanation:

Since we have given that

Number of boxes Jack can wrap = 28

Time taken by him = 2 hours

Number of boxes Walter can wrap = 36

Time taken by him = 3 hours

Work done by Jack in 1 hour is given by

`(2)/(28)\\\\=(1)/(14)`

Work done by Walter in 1 hour is given by

`(3)/(36)\\\\=(1)/(12)`

So, Work done by both Jack and Walter in 1 hour is given by

L.C.M. of
`((1)/(14),(1)/(12))` is
`=(l.c.m.\ of \ numerator)/(h.c.f\ of\ denominator)=(1)/(2)`

Number of units done by Jack is given by

`((1)/(2))/((1)/(14))\\\\=(14)/(2)\\\\=7\ units`

Number of units done by Walter is given by

`((1)/(2))/((1)/(12))\\\\=(12)/(2)\\\\=6\ units`

So, Let the number of hours be 't' .

`7t+6t=(1)/(2)* 65\\\\13t=(1)/(2)* 65\\\\t=(1)/(2)* (65)/(13)\\\\t=(5)/(2)\\\\t=2.5\ hours`

So, They work for 2.5 hours to gift wrap 65 boxes.