Question

Yogesh requires 3 days more than Vivek to do a work completely. If both

of them work together, the work can be completed in 2 days. Find the

number of days required for each of them to do the work completely.

Answer 1

Answer:

Step-by-step explanation:

Let days taken by Vivek be x

Days taken by Yogesh = x + 3

Work done by :

Vivek = 1/x

Yogesh = 1/(x + 3)

When they work together = 1/2

1/x + 1/(x + 3) = 1/2

(x + 3) + x = (x + 3)x/2

2(x + 3) + 2x = x^2 + 3x

2x + 6 + 2x = x^2 + 3x

x^2 - x - 6 = 0

Solving for x:

x^2 - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = - 2 or 3

We take the positive value.

Vivek = 3 days

Yogesh = 3 + 3 = 6 days

Answer 2

Answer:


Step-by-step explanation:

Let days taken by Vivek be x

Days taken by Yogesh = x + 3

Work done by :

Vivek = 1/x

Yogesh = 1/(x + 3)

When they work together = 1/2

1/x + 1/(x + 3) = 1/2

(x + 3) + x = (x + 3)x/2

2(x + 3) + 2x = x^2 + 3x

2x + 6 + 2x = x^2 + 3x

x^2 - x - 6 = 0

Solving for x:

x^2 - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = - 2 or 3

We take the positive value.

Vivek = 3 days

Yogesh = 3 + 3 = 6 days