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 = [tex] \frac{1}{2}*1000 = 500 [/tex]
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
[tex] b = 3 * \frac{1000}{2} [/tex]
Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.
Therefore,
[tex] b = 3 * \frac{g}{2} [/tex]
[tex] b = \frac{3}{2}g [/tex]
Cross multuply
[tex] 2b = 3g [/tex]
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:
[tex] \frac{3}{3} * 500 [/tex]
[tex] p = \frac{1500}{3} [/tex]
Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.
[tex] p = \frac{b}{3} [/tex]
Cross multiply
3p = b
The relation between the flow of water between different caps is required.
The relations are b = (3/2)g and p = (1/3)b
b = Rate of water flow through blue cap = 1500 gallons per minute
g = Rate of water flow through green cap = 1000 gallons per minute
p = Rate of water flow through purple cap = 1000/2 = 500 gallons per minute
We have the relation
[tex]1000\times 1.5=1500[/tex]
[tex]\Rightarrow g1.5=b[/tex]
[tex]\Rightarrow b=\dfrac{3}{2}g[/tex]
For second part
[tex]500 \times 3=1500[/tex]
[tex]\Rightarrow p3=b[/tex]
[tex]\Rightarrow p=\dfrac{1}{3}b[/tex]
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