Question

2 faucets can fill a tank in 1 hour and 20 minutes. The first faucet takes more than two hours longer to fill the same tank when functioning without the second tap. How long does it take to fill each one separately?

• A. $4$ hrs, $3$ hrs
• B. $4$ hrs, $2$ hrs
• C. $5$ hrs, $3$ hrs
• D. None of these

Answer 1

The correct option is B $4$ hrs, $2$ hrs

time needed by $2$nd faucet alone --- t hrs
rate for $2$nd faucet alone = $\frac{1}{t}$
time needed by $1$st faucet alone --- $t+2$ hrs
rate of 1st faucet along = $\frac{1}{(t+2)}$
combined rate = $\frac{1}{t}$ + $\frac{1}{(t+2)}$
= $\frac{(t+2+t)}{\left(t\right(t+2)}$ = $\frac{(2t+2)}{\left(t\right(t+2\left)\right)}$
= $4/3$
$\frac{t(t+2)}{(2t+2)}$ = $\frac{4}{3}$
$3t^2+6t=8t+8$
$3t^2-2t-8=0$
$(t-2)(3t+4)$ = $0$
t = $2$ or t = a negative time
the $2$nd faucet would take $2$ hours alone
the $1$st facucet would take $4$ hours alone