Chapter 8.6, Problem 54PPSE

Solution

To identify:The how many attendants working at the same rate should be hired so that the baseballs from 10 machines are all retrieved in less than 8 hours.An automatic pitching machine can pitch all its baseballs in $1\frac{1}{4}$ hours. One attendant can retrieve all the baseballs pitched by one machine in $3\frac{1}{2}$ hours.

The required number of attendants to retrieve the balls pitched by ten machines with in 8 hours is 5.

Given information:

The given isone attendant can retrieve all the baseballs pitched by one machine in $3\frac{1}{2}$ hours.

Explanation:

Consider the given information

Let $x$ is the number of attemdants required to retrieve the balls in $8$ hours.

One person takes $3.5$ hour to retrieve the balls pitched by one machine.

One person takes $3.5\times 10=35\text{hr}$ to retrieve the balls pitched by ten machine.

Rate of work of one person is $\frac{1}{35}$

Rate of work of $x$ persons is $\frac{x}{35}$

Time required to finish the work with the same rate for $x$ person is $\frac{35}{x}$ hours.

According to data.

  $\begin{array}{c}\frac{35}{x}=8\\ x=\frac{35}{8}\\ x\approx 5\end{array}$

Hence the required number of attendants to retrieve the balls pitched by ten machines with in 8 hours is 5.