Math Word Problem

Question

At the top of the Empire State Building, a woman's glasses accidently fall off her face while she was looking down. The equation relating h, the height above the ground in feet, and t, the time in seconds her glasses have been falling, is h = -16t^2 + 1,400. at the same time, a toddler tosses a ball over the edge of a railing, straight down to the ground. The equation for the ball is given by  h= -16t^2 - 24t + 1,400. By how many seconds does his ball beat the lady's glasses to the ground?

Answer 1

Both items will be at h = 0 when they reach the ground: 

Glasses:  h = - 16t² + 1,400
Now, using algebra, substitute a '0' value for 'h' and ADD a value of 16t² to both sides (right/left) of equation:  0 + 16t² = - 16t² + 16t² + 1,400 

and SIMPLIFY:  16t² = 1,400

Now, divide by a value of '16' on both sides (right/left) of this new equation:
  16t² / 16 = 1,400 / 16   so that  =>  t² = 87.5 

Finally, take the square root of both sides (right/left) of this equation:
 √ t² = √ 87.5  =>  using your calculator, you now have a numerical answer for 't' (in seconds) when the √ 87.5 is calculated.  

REPEAT these steps (beginning with h = 0) for the equation of the BALL, find a numerical answer for 't', and then COMPARE the 2 unique values for 't' in BOTH equations (i.e. t _BALL value compared to t _GLASSES value) ... the DIFFERENCE between the values of 't' will determine by how many seconds the toddler's ball beats the lady's glasses to the ground.