Question 1169855
 A cistern can be filled by two pipes.
 The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone.
let b = the larger pipe time to fill the cistern alone
then
(b+24) = time the small pipe to do it
let t = time required by the two pipes working together
let the completed job = 1
{{{t/b}}} + {{{t/((b+24))}}} = 1
:
 The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together.
t = (b+24) - 32
t = (b-8)
 How long will it take the larger pipe to fill the cistern alone.
{{{t/b}}} + {{{t/((b+24))}}} = 1
Replace t with (b-8)
{{{((b-8))/b}}} + {{{((b-8))/((b+24))}}} = 1
multiply equation by b(b+24)
(b-8)(b+24) + b(b-8) = b(b+24)
FOIL
b^2 + 24b - 8b - 192 + b^2 - 8b = b^2 + 24b
Cancel a b^2 and a 24b and we have
b^2 - 16b - 192 = 0
This will factor to
(b+8)(b-24) = 0
positive solution
b = 24 min for the large pipe to fill the cistern alone
:
:
Check this in the equation
{{{t/b}}} + {{{t/((b+24))}}} = 1
t = 24 - 8
t = 16 min together
and
24 + 24 = 48 min small pipe alone
{{{16/24}}} + {{{16/48))}}} = 1
{{{2/3}}} + {{{1/3}}} = 1