Chapter 11, Problem 60RE

To determine

To find: Here long will it take each of them woring alone to finish the job .

Explanation of Solution

Given information: Bruce and Bryce working together can complete the job in 1 hours and 20 minutes (i.e 80 minutes ).

So, Bruce and Bryce 1 minutes work is $\frac{1}{80}$

Similarly :

Bruce+ Bryce= $\frac{1}{80}$ .......(1)

Bruce+ marty= $\frac{1}{96}$ ......(2)

Marty+ Bruce $=\frac{1}{160}$ ......(3)

Adding equation (1),(2) and (3), we get

2[Bruce+ Bryce+ marty]= $\frac{1}{80}+$ $\frac{1}{96}+$ $\frac{1}{160}$

  $\Rightarrow$ 2[Bruce+ Bryce+ marty]= $\frac{7}{240}$

  $\Rightarrow$ Bruce+ Bryce+ marty= $\frac{7}{480}$ ......(4)

Now, from equation (1)

marty= $\frac{7}{480}$ $-$ $\frac{1}{80}$

marty= $\frac{1}{480}$

so, Marty can complete the job in $480$ minutes $=8$ hours

from equation (2)

Bryce $=\frac{1}{96}-\frac{1}{480}$

Bryce $=\frac{1}{120}$

So, Bryce the job in 120 minutes $=2$ hours

Now, from equation (3)

Bruce $=\frac{1}{160}-\frac{1}{480}$

Bruce $=\frac{1}{240}$

So bruce can complete the job in $240$ minutes $=4$ hours.