Question

Rob walks up to a tank of water that can hold 85 gallons. When it is active a drain

empties water from the tank at a constant rate. When Bob first sees the tank it
contains 30 gallons of water. 5 minutes later, the tank contains 15 gallons of water.

Answer 1

rate of change: 3 gal/min

minutes to empty: 5 minutes

minutes before Bob arrived that tank was full: 18 1/3 minutes

Explanation:

When Bob first saw it, the tank contained 30 gal. 5 minutes later it contained 15 gal.

Difference in gallons: 30 - 15 = 15

Difference in time: 5 minutes

Rate of draining: 15 gal / 5 minutes = 3 gal/minute

It drained 15 gallons in 5 minutes. It has 15 gallons now, so it will take 5 minutes to empty out.

The total capacity is 85 gallons. When Bob saw it, it only had 30 gallons.

85 gal - 30 gal = 55 gal

It had emptied 55 gallons before Bob saw it.

emptying rate = volume/time

time = volume/rate

time = 55 gal / (3 gal/min)

time = 55/3 minutes

time = 18 1/3 minutes