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. What is the equation in fraction form

Answer 1

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

`\dot Q_(purple) = (1)/(2)\cdot \dot Q_(green)`

Explanation:

The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.

`\dot Q_(i) = k \cdot \dot Q_(j)`

There are two different solutions:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

`\dot Q_(purple) = (1)/(2)\cdot \dot Q_(green)`

Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):

`\dot Q_(purple) = (1)/(2) * (1000\,gpm)/(1500\,gpm)\cdot \dot Q_(blue)`

`\dot Q_(purple) = (1)/(3)\cdot \dot Q_(blue)`