Question 311925
Let filling the tank be 1 job.

two pipes do the job in 10 hours
they do 1/10 of the job in 1 hour
.
one pipe alone does in x hours.
so it does 1/x of the job in 1 hour.
.
the other pipe does in x+15 hours
so it does 1/ x+15 of the job in 1 hour
.
1/x + 1/ x+15 = 1/10

x+15+x / x(x+15) = 1/10
2x+15 /x(x+15)= 1/10
10(2x+15)=x(x+15)
20x+150=x^2+15x
x^2+15x-20x-150=0
x^2-5x-150=0
x^2-15x+10x-150=0
x(x-15)+10(x-15)=0
(x-15)(x+10)=0
x=15
one pipe does it in 15 hours
the other does it in 30 hours
..