Question 551349
let Man take x hours to complete the job alone
so he does 1/x of the job in 1 hour

woman takes 1/(x+2) hours to do the same job
so she does 1/(x+2) of the job in 1 hour

Together they can do 1/x + 1/(x+2) of the job in 1 hour
add up both
=(2x+2)/x(x+2) 

so they take x(x+2)/(2x+2) hours

x(x+2)/(2x+2)= 10
x(x+2)=10(2x+2)
x^2+2x=20x+20
x^2-18x-20=0
x^2-20x+2x-20=0
x(x-20)+2(x-20)=0
(x-20)(x+2)=0
Take the positive value
x= 20 

Man takes 20 hours
Woman takes 20 +2 = 22 hours
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1/6 +1/8 - 1/10 is the job done in 1 hour ( filling the pool)
7/24 - 1/10
Addup
(70-24)/240
46/240 of the job is done in 1 hour
so it will take 240/46 hours = 5.2 hours

HAPPY NEW YEAR