Question

Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone. Solve the word problem

Answer 1

Hi ,

Let Nishu alone complete the work in x days.

portion of work done by Nishu in day = 1/x

Pinku alone complete the work in ( x + 6 ) days

portion of the finished

by Pinku in a day = 1/( x + 6 )

They together finish the work in 4 days.

portion of work finished by them in a day = 1/4

Therefore ,

1/x + 1/( x + 6 ) = 1/4

( x + 6 + x )/[ x( x + 6 ) ] = 1/4

( 2x + 6 )/( x² + 6x ) = 1/4

4( 2x + 6 ) = x² + 6x

8x + 24 = x² + 6x

x² - 2x - 24 = 0

splitting the middle term , we get

x² - 6x + 4x - 24 = 0

x( x - 6 ) + 4( x - 6 ) = 0

( x - 6 )( x + 4 ) = 0

x - 6 = 0 or x + 4 = 0

x = 6 or x = -4

x should not be negative.

x = 6

Nishu finish the work alone in 6 days.

Pintu finish the work alone in 12 days.

I hope this helps you.

: )