Question

A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap.
Part A Write an equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.

Part B Write an equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.

Answer 1

Answer:

a) 2b = 3g

b) 3p = b

Step-by-step explanation:

Given:

Fire hydrant with a blue cap, b, provides water at a rate = 1500 gallons per min

Fire hydrant with a green cap, g, provides water at a rate = 1000 gallons per min

Fire hydrant with a purple cap, p, provides water at a rate = ½g = $\frac{1}{2}*1000 = 500$

a) The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.

Given flow of blue hydrant, b = 500

Simplifying, we have:

b = 3*500

$b = 3 * \frac{1000}{2}$

Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.

Therefore,

$b = 3 * \frac{g}{2}$

$b = \frac{3}{2}g$

Cross multuply

$2b = 3g$

The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g is 2b=3g.

b) An equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.

Given flow rate of purple hydrant, p = 500

It could also be re-written as:

$\frac{3}{3} * 500$

$p = \frac{1500}{3}$

Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.

$p = \frac{b}{3}$

Cross multiply

3p = b