A hose can fill up a pool in \( 6 \) hours. Another hose requires \( 3 \) more to fill the pool than the two hoses together. How long does it take the second hose to fill the pool?
A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool. ---------------- h1 takes 6 hours, so it fills 1/6 pool per hour. h2 takes x hours, so it fills 1/x pool per hour. Together, they do 1/6 + 1/x per hour. 1/6 + 1/x = (x+6)/6x per hour (together), so it takes 6x/(x+6) hours. -------------------
The time the 2nd hose takes, x hours, is 3 hours more than the time together. x-3 = 6x/(x+6) (x-3)*(x+6) = 6x (x-6)*(x+3) = 0 x = 6 hours (Ignore the -3 hours) ----------- Each hose takes 6 hours. Together they take 3 hours, so the time for the 2nd hose is 3 hours more than the 3 hours together.