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.
Answers
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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