Two pipes together can fill a tank in $\frac{15}{8}$ hours. The pipe with larger diameter takes $2$ hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which e

Question

Two pipes together can fill a tank in $\frac{15}{8}$ hours. The pipe with larger diameter takes $2$ hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.

Accepted Answer

Step 1: Let the time taken by smaller diameter tap $= x$ hrs.
Larger diameter tap $= (x - 2)$ hrs.
$\frac{1}{x - 2} + \frac{1}{x} = \frac{8}{15}$
Step 2: $\Rightarrow 15(2x - 2) = 8x(x - 2)$
$\Rightarrow 8x^2 - 46x + 30 = 0$
$\Rightarrow 4x^2 - 23x + 15 = 0$
$\Rightarrow (4x - 3)(x - 5) = 0$
Step 3: $x = \frac{3}{4}$ or $x = 5$. Since $x 
eq \frac{3}{4}$ (as $x - 2 < 0$):
Smaller diameter tap fills in $5$ hrs, larger diameter tap fills in $3$ hrs.

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