We can use the formula D=rt where D= distance, r= rate and t= time to determine the distance a horse covers in a particular amount of time.

Question

We can use the formula  where  distance,  rate and  time to determine the distance a horse covers in a particular amount of time.

If we solve this equation for time (), so we can determine our length of time needed for the horse to run a set distance, we get:

The distance of the steeplechase is 3000 meters so we now have:

For this assignment you will graph the function above. How do the horse’s time and speed vary with respect to each other? Explain mathematically, why we cannot figure out the horse’s time if its speed is 0 meters per second. How fast do you believe your horse would need to run to win a race?

Answer 1

Yes, if you solve for t then you get t = 3000/r

Or it may be easier to visualize as

3000 = tr

In either case you do not have a direct, but inverse relationship. So if the time gets longer, the rate (speed) will get smaller.

When the horse is standing still (r = 0) it will cover no distance and it will take an infinite time to cover 3000m. As you should know from algebra, if there is zero in a fraction denominator, the result is undefined. Using your math equation, t = 3000/0 is undefined and you cannot calculate the time.

As for graphing, you would graph rate vs time, usually putting r on the y axis and t on the x axis. The equation would be r = 3000m/t . This of course will not be a straight line. for (t,r) pairs you can see from (1,3000), (10, 300), (100, 30) and and (1000, 3). As time becomes longer, the speed decreases asymptotically toward zero.