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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?

Verified Answer :

serinasantiago

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

Step-by-step 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

\(\frac{2}{28}\\\\=\frac{1}{14}\)

Work done by Walter in 1 hour is given by

\(\frac{3}{36}\\\\=\frac{1}{12}\)

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

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

Number of units done by Jack is given by

\(\frac{\frac{1}{2}}{\frac{1}{14}}\\\\=\frac{14}{2}\\\\=7\ units\)

Number of units done by Walter is given by

\(\frac{\frac{1}{2}}{\frac{1}{12}}\\\\=\frac{12}{2}\\\\=6\ units\)

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

\(7t+6t=\frac{1}{2}\times 65\\\\13t=\frac{1}{2}\times 65\\\\t=\frac{1}{2}\times \frac{65}{13}\\\\t=\frac{5}{2}\\\\t=2.5\ hours\)

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