college algebra help?

Question

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until the sound is heard. if t1 is the time measured in seconds that it takes for the object to strike the water, then t1 will obey the equation s=16t(2/1) where "s" is the distance in feet. It follows that t1=(sq. root of s/4) Suppose that t2 is the time that it takes for the sound of the impact to reach your ears. Because sound waves are known to travel at a speed of approx. 1100 ft per second, the time t2 to travel the distance "s" will be t2=(s/1100) Now t1+t2 is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard. We have the equation - Total time elapsed = (sq. root of s/4) + (s/1100) ... now find the distance to the water's surface if the total time elapsed from dropping a rock to hearing it hit the water is 4 seconds

Answer 1

Total time elapsed = (sq. root of s/4) + (s/1100)
t = √s/4 + s/1000
4 = √s/4 + s/1000
0 = 1/1000 * s + 1/4 * √s - 4

You can use the quadratic equation for √s in this instance, because it's a polynomial in terms of √s (1/1000 √s^2 + 1/4 √s - 4):
√s = (-b +/- (b^2 - 4ac)^(1/2))/2a
√s = (-1/4 +/- (1/16 + 16/1000)^(1/2))/(2/1000)
√s = -125 +/- 140.09 = 15.09 or -265.09 - ignore negative number.
s = 227.7 ft.

Check:
t = √s/4 + s/1000
4 = 15.09/4 + 227.7 / 1000
f = 3.7725 + .2277 = 4.0002 (check!)