Chapter 11.5, Problem 50PPE

To determine

We have to find “time”

Answer to Problem 50PPE

  $\frac{1200}{51}\min or23.5\min$

Explanation of Solution

Given:

  $mike=75\min ,joan=60\min ,kyle=80\min$

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Then total work divided by total efficiency (formula=total efficiency*total time=total work)

Calculation:

In order to calculate time, firstly we have to take LCM of all given parameters

  $mike\text{}=75\min ,joan=60\min ,kyle=80\min$

  $TimeWorkEfficiency$

  $mike7516$

  $joan60120020$

  $kyle8015$

  $(LCM)(efficiency\text{}=\text{}\frac{work}{time})$

  $totaltime=\frac{totalwork}{efficiency}$

  $\frac{1200}{16+20+15}=\frac{1200}{51}=\frac{400}{17}\min or23.5\min$

Thus, the solution is correct.