Time and Work Examples 2

In this class, We discuss Time and Work Examples 2.

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Example 1:

Two men and Three boys can do work in 10 days.

Three men and two boys can do the same work in 8 days.

How many days can two men and one boy do the same work?

Solution:

Identify one man’s one-day capability and one boy’s one-day capability.

One man one-day work = x

One boy one-day work = y

2x + 3y one days work = 1/10

2x + 3y = 1/10

3x + 2y = 1/8

Solve the equations and find x and y.

x = 7/200

y = 1/100

(2 men + 1 boy).’s one day work = (2 * 7/200 + 1 * 1/100)

= 16/200 = 2/25

(2 men + 1 boy) can finish the work in 25/2 days.

= 12 1/2 days

Example 2:

One man, three women, and four boys can do a piece of work in 96 hours.

Two men and eight boys can do the same work in 80 hours.

Two men and three women can do it in 120 hours.

Five men and 12 boys can do it?

Solution:

One man 1 hours work = x

1 woman 1 hours work = y

One boy 1 hours work = z

x+ 3y + 4z = 1/96 – equation 1

2x + 8z = 1/80 – equation 2

2x + 3y = 1/120 – equation 3

Add 2 and 3 and subtract 1

3x + 4z = 1/96 – equation 4

From equation 2 and 4 we get x = 1/480

Substitution we get y = 1/720 and z = 1/960

(5 men + 12 boys).’s one day work = (5/480 + 12/960) = 11/480

They can finish the work in 480/11 hours

= 43 7/11 hours.