Chapter 8.6, Problem 36PPSE

Solution

To identify:How long will it take to complete the calls working together.You and a classmate have volunteered to contact every member of your class by phone to inform them of an upcoming event. You can complete the calls in six days if you work alone. Your classmate can complete them in four days.

If Nis the number of calls, what expression represents the number of calls at you can make per day? What expression represents the number of calls your friend can make per day?

• What is the expression for the number of days needed to make N calls if you are working together?

The number of days required to complete the calls working together is $1.2\text{days}$ .

Given information:

The given is you can complete the calls in six days if you work alone. Your classmate can complete them in four days.

Explanation:

Consider the given information

The number of calls that you both can do per day is

  $\begin{array}{c}\frac{N}{6}+\frac{N}{4}=\frac{4N+6N}{12}\\ =\frac{10N}{12}\\ =\frac{5N}{6}\end{array}$

Thus the number of calls that can be done by both of you in one day is $\frac{5N}{6}$

The $N$ calls can be finished if both people work together in $\frac{6}{5}\text{days}=1.2\text{days}$ .

Hence the number of days required to complete the calls working together is $1.2\text{days}$ .