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 =
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}](https://tex.z-dn.net/?f=%20b%20%3D%203%20%2A%20%5Cfrac%7B1000%7D%7B2%7D%20)
Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.
Therefore,
![b = 3 * \frac{g}{2}](https://tex.z-dn.net/?f=%20b%20%3D%203%20%2A%20%5Cfrac%7Bg%7D%7B2%7D%20)
![b = \frac{3}{2}g](https://tex.z-dn.net/?f=%20b%20%3D%20%5Cfrac%7B3%7D%7B2%7Dg%20)
Cross multuply
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](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B3%7D%20%2A%20500%20)
![p = \frac{1500}{3}](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7B1500%7D%7B3%7D%20)
Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.
![p = \frac{b}{3}](https://tex.z-dn.net/?f=%20p%20%3D%20%5Cfrac%7Bb%7D%7B3%7D%20)
Cross multiply
3p = b