Examples of Chain Rule 3

In this class, We discuss Examples of Chain Rule 3.

The reader should have prior knowledge of chain rule basic examples. Click Here.

Example 1:

Two men and seven boys can do a piece of work in 14 days.

Three men and eight boys can do the same in 11 days.

Eight men and six boys can do three times the amount of work in how many days.

Solution:

(2 * 14) men + (7 * 14) boys = (3 * 11) men + (8 * 11) boys

5 men = 10 boys

1 man = 2 boys

2 men + 7 boys = (2 * 2) + 7 = 11 boys

8 men + 6 boys = (8 * 2) + 6 = 22 boys

More boys Fewer days – indirectly proportional

More work, more days – directly proportional

The below diagram shows the proportion.

22 * 1 * x = 11 * 3 * 14

x = 21

Example 2:

Three men or six boys can do a piece of work in 10 days, working 7 hours daily.

How many days will it take to complete a piece of work twice as large as with six men and two boys working 8 hours a day?

Solution:

3 men = 6 boys

6 men + 2 boys = 14 boys

More work, more days – Directly proportional

More boys fewer days – Indirectly Proportional

More hours fewer days – Indirectly proportional

The below diagram shows the proportion.

1 * 14 * 8 * x = 2 * 6 * 7 * 10

x = 840/112