55% of 20 is 11. the answer is 20
Given the table showing the distance Randy drove on one day of her vacation as follows:
![\begin{tabular} {|c|c|c|c|c|c|} Time (h)&1&2&3&4&5\\[1ex] Distance (mi)&55&110&165&220&275 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0ATime%20%28h%29%261%262%263%264%265%5C%5C%5B1ex%5D%0ADistance%20%28mi%29%2655%26110%26165%26220%26275%0A%5Cend%7Btabular%7D)
The rate at which she travels is given by
![rate= \frac{distance}{time} \\ \\ = \frac{55}{1} =55mi/h](https://tex.z-dn.net/?f=rate%3D%20%5Cfrac%7Bdistance%7D%7Btime%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B55%7D%7B1%7D%20%3D55mi%2Fh)
If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by
distance = 55 x 6 = 330 miles.
The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft
50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt