# math

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A does 8/15 of a work in 8 days and the remaining work is finished with the assistance of B in 4 days . how long will B take to do the work alone

• math -

A's rate = (8/15)W / 8 = W/15
let B's rate = W/x , where x is the time it would take B to do the job

combined rate = W/15+W/x = (Wx + 15W)/(15x)

then 4(Wx + 15W)/(15x) = (7/15)W
divide by W and expand
(4x + 60)/(15x) = 7/15
times 15
(4x+60)/x = 7
multiply by x
4x + 60 = 7x
x = 20

it would take B 20 days

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