Question

A can do a piece of
work in x days and
B can do it in (x+16 ) days. If both working
together can do it in 15 days, find x​

Answer 1

Step-by-step explanation:

work done by A in 1 day =1/x

work done by B in 1 day =1/x+16

Work done by A+B in 1 day =1/15

$\frac{1}{x} + \frac{1}{x + 16} = \frac{1}{15} \\ \frac{x + x + 16}{x(x + 16)} = \frac{1}{15} \\ \frac{2x + 16}{ {x}^{2} + 16} = \frac{1}{15} \\ 15(2x + 16) = {x}^{2} + 16 \\ 30x + 240 = {x}^{2} + 16 \\ {x}^{2} - 30x - 240 + 16 = 0 \\ {x}^{2} - 30x - 224 = 0 \\ from \: here \: x = 14 \: and \: 16$