Posted by **Grant** on Tuesday, May 14, 2013 at 7:28am.

Fuel is flowing into a storage tank which can be filled to a depth of 6 metres.

When the fuel started flowing the tank was already filled to a depth of 2.5m. If the rate at which the depth of fuel in the tank is increasing, in metres per hour is given by d'(t) = 4t +5, find:

(i) the rate at which the height is increasing after 20 minutes

(ii) the height of water in the tank after 20 minutes

(iii) the time it takes to fill the tank

- Calculus -
**Reiny**, Tuesday, May 14, 2013 at 9:54am
Let the depth of the water be d(t)

if d ' (t) = 4t+5 , where t is in hours

d(t) = 2t^2 + 5t + c, where c is a constant

given: when t=0, d(0) = 2.5

2.5 = 0 + 0 + c , ----> c = 2.5

d(t) = 2t^2 + 5t + 2.5

a) when t = 20 min, t = 1/3 hrs

d ' (1/3) = 4(1/3) + 5 = 19/3 m/hr

b) after 20 min or after 1/3 hr

d(1/3) = 2(1/9) + 5(1/3) + 2.5 = 79/18 or appr 4.39 minutes

c) to fill the tank ...

2t^2 + 5t + 2.5 = 6

2t^2 + 5t - 3.5 = 0

by the formula ...

t = (-5 ± √53)/4

= .57 hrs or a negative time, which we will reject

.57 hrs = 34.2 minutes

## Answer this Question

## Related Questions

- Calculus - Fuel is flowing into a storage tank which can be filled to a depth of...
- AP CALCULUS!!! HELPP - related rates: the base of a pyramid-shaped tank is a ...
- AP CALCULUS!! HELPPP URGENT - related rates: the base of a pyramid-shaped tank ...
- solid mensuration - A cylindrical tank with flat ends has a diameter of two ...
- calculus - Water is flowing freely from the bottom of a conical tank which is 12...
- math - Ben placed a stone in an empty rectangular tank, 50cm long and 40cm wide...
- Physics - A water tank is filled to a depth of 10 m, and the bottom of the tank ...
- Math - A bus driver filled up 7/8 fuel tank for a trip. She used 6/7 of the fuel...
- AP calculus - The base of a cone-shaped tank is a circle of radius 5 feet, and ...
- geometry - A satellite launch rocket has a cylindrical fuel tank. The fuel tank ...

More Related Questions