Question

Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company picnic, and they only completed 112 packages. Today, his department will complete 43 packages per hour. If Matthew wants to complete packages at an average rate of at least 39 packages per hour, then what is the minimum number of hours that the department must operate today to compensate for yesterday's company picnic?

Answer 1

Alright, lets get started.

If Matthew wants to complete packages at an average rate of at least 39 packages per hour.

And they worked 4 hrs only due to picnic, yesterday, it means they have to make $39*4 = 156$ packages.

But they made only 112 packages means they are short of $156 - 112 = 44$ packages.

Suppose they are working today t hrs, and his department will complete 43 packages per hour today.

It means they are going to make 43 t packages today.

This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.

So, average will be

$\frac{43 t - 44}{t} = 39$ (39 average given in question)

Cross multiplying

$39 t = 43 t - 44$

Adding 44 in both sides

$39 t + 44 = 43 t - 44 + 44$

$43 t = 39 t + 44$

Subtracting 39 t in both sides

$43 t - 39 t = 39 t + 44 - 39 t$

$4t = 44$

Dividing 4 in both sides

t = 11 hrs

Hence they have to woth 11 hrs today : Answer

Hope it will help :)

Answer 2

Number of packages per hour is 11