Chapter 6.3, Problem 36PPS

To determine

The liters of water that the sprinkler system can pump in $\frac{1}{4}$ minute.

Answer to Problem 36PPS

The sprinkler system pumps up to $14.19$ litres of water in $\frac{1}{4}$ minute.

Explanation of Solution

Given information:

The sprinkler system pumps up to $1500$ gallons of water per minute.

Formula used:

Conversion rule to convert gallons into litres which is expressed as,

  $1\text{gallon}=3.785\text{litres}$

Calculation:

Consider the provided statement “The sprinkler system pumps up to $1500$ gallons of water per minute.”

Recall conversion rule that 1 gallon is $3.785$ litres.

So, $1500$ gallons is evaluated as when $1500$ is multiplied by $3.785$ .

Therefore, $1500$ gallons is,

  $\begin{array}{c}1\text{gal}=3.785\text{L}\\ 1500\text{gal}=\left(15\times 3.785\right)\text{L}\\ 1500\text{gal}=56.775\text{L}\end{array}$

The sprinkler system pumps $56.775$ litres of water per minute.

Now,litres that sprinkler system can pump in $\frac{1}{4}$ minute will be evaluated as when $56.775$ is multiplied by $\frac{1}{4}$ .

Therefore, in $\frac{1}{4}$ minute water pumped by the system is,

  $\begin{array}{c}1\min =56.775\text{L}\\ \frac{1}{4}\min =\left(56.775\times \frac{1}{4}\right)\text{L}\\ \frac{1}{4}\min =14.193\text{L}\end{array}$

Rounding off to the nearest hundredth,

  $\frac{1}{4}\min =14.19\text{L}$

Hence,the sprinkler system pumps up to $14.19$ litre of water in $\frac{1}{4}$ minute.