Duke can wrap 47 gifts per hour, and Iris can wrap 29 gifts per hour. If they work together how long will take them to wrap 456 gifts?

Answer 1

Simply add Duke and Iris' Rates: 47 + 29 = 76

That means together, they can make 76 gifts an hour

So to make 456 gifts, they simply need 456/76 = 6 hours

Answer 2

First, ask yourself how many gifts can Duke and Iris wrap per hour, working together.

Answer: 47 + 29 = 76

There are several ways to solve the original problem at this point, but proportions (two fractions connected with an equal sign) are so useful in so many situations that let's do it that way.

So, the rate that Duke and Iris can wrap gifts together is 76 gifts per hour. We can write that as a fraction.

76 gifts

-----------

1 hour

Then, we set that fraction equal to another fraction, using the number of gifts needed to be wrapped, as given in the original problem. We will use H as our unknown, standing for the number of hours that Duke and Iris would take to wrap 456 gifts. Thus, we have the following proportion:

76 gifts 456 gifts

----------- = -------------

1 hour H hours

Solve this, using cross-multiplication to get your answer. It will be expressed in hours.