Question

Two pipes can fill a tank in 19 minutes if both are turned on. If only one is used, it would take 49 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)

Answer 1

Answer:

The time taken by smaller pipe to fill the tank alone is 74.2 min

Step-by-step explanation:

Given as :

The time taken by two pipes to fill tank = 19 min

Let the time taken by larger pipe to fill tank = y

And the time taken by smaller pipe to fill tank = x

According to question

The smaller pipe takes 49 minutes longer than larger pipe

I.e x = y + 49

Now,

$\dfrac{1}{x}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{1}{y + 49}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{y + 49 + y}{y^{2} + 49 y }$ = $\dfrac{1}{49}$

Or, 2 y + 49 = $\dfrac{y^{2}+49y }{19}$

Or, 19 × ( 2 y + 49 ) = y² + 49 y

Or, 38 y + 931 = y² + 49 y

Or, y² + 49 y - 38 y - 931 = 0

or, y² + 11 y - 931 = 0

Or, Applying quadratic equation method to calculate the value of y

so, y = $\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or,  y = $\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}$

Or, y = $\frac{- 1 \pm \sqrt{121+3724}}{2}$

or, y = $\frac{- 1 \pm \sqrt{3845}}{2}$

or, y = $\frac{- 1 \pm 62.008}{2}$

∴   y = 25.2 , - 36.5

So, The time taken by larger pipe = y = 25.2 min

and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min

Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer