You can calculate the average speed by dividing the distance by time
= (3x220/33)yards/sec = (220/11)yards/sec
= 20 yards/sec
A racehorse is running a 10-furlong race. (1 furlong = 220 yards)
As the horse passes each furlong marker (F), its time is recorded.
F| 0 1 2 3 4 5 6 7 8 9 10
T| 0 20 33 46 59 73 86 100 112 124 135
a) What is the approx speed of the horse as it passes the 3rd marker?
(Do I need to come up with an equation?...and find the derivative, to get the speed at that point?)
The 'average rate of change' can be calculated from the data. One way to do this is to say the horse has gone 660 yards in 46 seconds, which would be 14.35 yards per second (you can convert units to mph if you want). This would represent the average speed over the first 3 furlongs. A better approximation might be to look at the average speed between the 2nd and 4th furlong markers. It took the horse 26 seconds to cover that 440 yards, which would indicate a speed of only 16.92 yards per second.
It looks like the horse is losing speed over this first part of the race!