Question

Question 17
Question
2) If 2 men works together then they can do the work in 12 hours. If 1 men
do the work 10 hours faster than the other. How many hours does it take
the second man to do the work?
Note: enter only the number as answer.
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Answer 1

1 man= 10 hr

2 man=20-12=8 hr

Answer 2

Given:

2 men work together then they can do the work in 12 hours.

If 1 man  do the work 10 hours faster than the other

To find:

How many hours does it take  the second man to do the work

Solution:

Let

number of hours taken by A to complete the work = x hours

Amount of work done by A in 1 hour = 1/x

number of hours taken by B to complete the work = y hours

Amount of work done by B in 1 hour = 1/y

Given that

A does the work 10 hours faster than the other

x = y + 10     (1)

A and B can do the work together in 12 hours. Therefore, in one hour they will do 1/12th of the work.

$\frac{1}{x} + \frac{1}{y} = \frac{1}{12}$     (2)

Now, we will solve these two equations to find the values of x and y.

Putting the value of x from (1) into (2) we get an equation

$\frac{1}{y + 10} + \frac{1}{y} = \frac{1}{12}$

= $y^2 - 14y - 120$

we will use splitting the middle term method to find the factors

= $y^2 - 20y + 6y - 120$

= $(y + 6) ( y - 20)$

From this, we will get y = -6, 20

we will take the positive value. Therefore, y = 20

The second man will take 20 hours to complete the work.