Determine time to drain water from tub

[ab5490]

Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is represented by the equation L = −5t2 – 8t + 120, where L represents the number of liters of water in the bathtub and t represents the amount of time, in minutes, since the plug was pulled.

1) How many liters of water were in the bathtub when Barb pulled the plug? Show your reasoning.

2) Determine, to the nearest tenth of a minute, the amount of time it takes for all the water in the bathtub to drain.

 

[jonboy]

Whenever the plug is pulled there has been zero minutes since it's been pulled. Since t = the amount of minutes since the plug was pulled, t = 0 initially.

How many liters of water were in the bathtub when Barb pulled the
plug?

This means we fill in 0 for t: \(\displaystyle \L \;L=\,-\,5(0)^{2}\, - \,8(0)\,+\,120\)

Solve for L, since that's the amount of number of liter in the tub.

To find the time it takes to drain the tub follow jwpaine.

 

[jwpaine]

To show the amount of water (L) in the tub before you pull the plug (0 seconds) substitute 0 for T and solve for L

To find the total time it took to drain, substitute 0 in for L (tub is empty) and then use the quadratic formula to find the value for T (time it took to drain)