Chapter 6, Problem 11MPS

To determine

To Solve:

The given problem.

Answer to Problem 11MPS

11:36 A.M.

Explanation of Solution

Given:

Given statement is :

Marie can prepare the salads at the Lunch Inn in 2 h .Bob needs 3 h to prepare the salads.At 10:00 A.M. Marie began the job. At 11:00 A.M. Bob joined her.At what time did they finish preparing the salads?

Calculation:

Let the total number of salads to be made are 6 [ LCM(2,3)].

Since Marie can prepare the salads in 2 h.

So, her efficiency is $\frac{work}{time}=\frac{6}{2}=3$

That is , Marie can prepare 3 salads per hour.

Since Bob can prepare the salads in 3 h.

So, his efficiency is $\frac{work}{time}=\frac{6}{3}=2$

That is , Bob can prepare 2 salads per hour.

Hence, Marie and Bob together can prepare 5 salads per hour.

Marie starts work at 10:00 A.M. and works alone till 11:00 A.M.

So, she works alone for 1 hour.

Hence, she completes 3 salads .

The total number of salads to be prepared are 6.

So, left are 3 salads to be prepared , that will be completed by Marie and Bob working together.

Since they together can complete 5 salads per hour.

Let they can complete 3 salads in x hours:

  $\begin{array}{l}\frac{5\text{ salads}}{1\text{ hour}}=\frac{3\text{ salads}}{x\text{ hours}}\\ \Rightarrow \frac{5}{1}=\frac{3}{x}\\ \Rightarrow 5x=\mathrm{3.................}[\text{multiply each side by x]}\\ \Rightarrow \frac{5x}{5}=\frac{3}{5}\mathrm{...............}[\text{divide each side by 5]}\\ \Rightarrow x=\frac{3}{5}\cdot 60\text{ minutes}\mathrm{...........}[1h=60\min utes]\\ \Rightarrow x=36\text{ minutes}\end{array}$

So, they take 36 minutes to complete 3 salads and they started at 11:00 A.M.

So, they will finish preparing the salads at 11:36 A.M.