Question

Jerry is filling a water tank which initially consists of 75 gallons of water. As the water is being pumped in, the water in the tank increases by 2.5 gallons every minute. To ensure that the tank does not overflow, he wants to fill the tank with a maximum of 195.5 gallons.

What is the maximum amount of time, in minutes, that Jerry can fill the tank without it overflowing?

Answer 1

48.2 minutes

Explanation:

With an increase of 2.5/min,

The volume is:

75 + 2.5t,

Where t is time (in minutes)

To aviod overflow:

75 + 2.5t 《 195.5

2.5t 《 120.5

t 《 48.2

Answer 2

The maximum amount of time is 48.2 minutes

Explanation:

We can use the equation for a line

y = mx+b

the inital value is 75 gallons ( that is b)

the slope is 2.5 gallons (that is m)

We know that we want to fill it to 195.5 gallons ( that would be y)

195.5 = 2.5x +75

We are going to solve for x (that is the number of minutes)

Subtract 75 from each side

195.5-75 = 2.5x +75-75

120.5 = 2.5x

Divide by 2.5 on each side

120.5/2.5 = 2.5x/2.5

48.2 =x

The maximum amount of time is 48.2 minutes