Question

Yogesh requires 3 days more than vivek to do work complete. If both work together can complete in 2 days . Find the days required for each of them to complete work.

Answer 1

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Answer 2

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Answer:

Vivek = 3 days

Yogesh = 6 days

Step-by-step explanation:

Define x:

Let x be the number of days Vivek needed to complete the work

1 day = 1/x of the work

Yogesh needed 3 days more than Vivek

Yogesh = x + 3

1 day = 1/(x + 3) of the work

Find the number of days needed if they work together:

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

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

1 day = (2x + 3)/(x² + 3x)

Number of days = (x² + 3x)/(2x + 3)

Solve x:

They need 2 days if they worked together:

(x² + 3x)/(2x + 3) = 2

(x² + 3x) = 2(2x + 3)

x² + 3x = 4x + 6

x² - x - 6 = 0

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

x = 3 or x = - 2(rejected, since it cant be negative(

Find the numbers of days required by each of them:

Vivek = x = 3 days

Yogesh = x + 3 = 3 + 3 = 6 days