Question 322519
Rate*Time=Output
.
.
.
1.{{{(RL+RS)40=Z}}}
where Z is the volume of the pool, RL is the rate of the large hose, RS is the rate of the small hose.
.
.
2.{{{RL*60=Z}}}
Setting equations 1 and 2 equal to each other,
{{{(RL+RS)40=RL*60}}}
{{{40*RL+40RS=60*RL}}}
{{{40RS=20RL}}}
{{{RL=2*RS}}}
Substituting into eq. 2,
{{{2RS*60=Z}}}
{{{RS*120=Z}}}
It would take the small hose 120 minutes to fill the pool alone.