Honors Problem 8

Question

Darrell and Angie need to wrap 60 small presents for their holiday party. In half an hour, Angie wraps twice as many presents as Darrell, and they have completed wrapping half of the presents. If he keeps working at the same rate, how long will it take Darrell to finish the wrapping by himself?

Answer 1

Let x be the time it would take Darrell to wrap all of the presents by himself. The rate at which he works is 60/x. Angie wraps twice as fast, so her rate is 120/x. Together, they have wrapped 30 presents in 1/2 an hour. This means,

 

30 = (their rate together)(their time) = (60/x + 120/x)(1/2) = (180/x)(1/2) = 90/x.

 

This means that 30 = 90/x. Solving for x: 30x = 90, so x = 3. Thus, Darrell can wrap all of the presents in 3 hours.