A and b can complete a task together in 35 days if a works alone and completes 5/7 of the task and then leaves the rest for b to complete by herself it will take a total of 90 days to complete the task how many days would it take a the move efficient amont the duo to complete the entire work by hereself
Answers
Define x and y:
Let x be the amount of days needed for A to complete the work alone
Let y be the amount of days needed for B to complete the work alone
They take 35 days to complete the work together:
1/x + 1/y = 1/35
35(x + y) = xy
35x + 35y = xy --------------------- [ 1 ]
They take 90 days if A did 5/7 of the work and B the remaining:
5/7 x + 2/7 y = 90
5x + 2y = 630
2y = 630 - 5x
y = 315 - 5/2 x --------------------- [ 2 ]
The two equations are:
35x + 35y = xy --------------------- [ 1 ]
y = 315 - 5/2 x --------------------- [ 2 ]
Sub [ 2 ] into [ 1 ]:
35x + 35( 315 - 5/2 x) = x (315 - 5/2 x)
35x + 11025 - 175/2 x = 315x - 5/2 x²
5/2 x² - 735/2 x + 11025 = 0
5x² - 735x + 22050 = 0
x² - 147x + 4410= 0
(x - 42)(x - 105) = 0
x = 42 or x = 105
Find y:
If x = 42
y = 315 - 5/2 (42) = 210
if x = 105
y = 315 - 5/2 (105) = 52.5
⇒ rejected, given that A is more efficient than B
Answer: A will need 42 to complete the work alone.