Question

EMERGENCY HELP! A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?

Answer 1

Answer:

$y=9x+33$

33 gallons of water to begin with.

Step-by-step explanation:

So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

The slope is:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9$

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

$y-y_1=m(x-x_1)\\y-87=9(x-6)\\y-87=19-54\\y=9x+33$

So, there were 33 gallons of water in the tank to begin with.