a Use the Speed Formula to determine the runner's rate before forming an inequality that uses this number.
B
b Usain Bolt's world record for a 200m dash, set in 2009, is 19.19s.
A
aInequality: r>40/7
Graph:
B
b No, see solution.
Practice makes perfect
a In order to write an inequality representing any speed faster than the runner's speed, first we need to determine what that speed is.
Determining the Runner's Speed
Let's find the runner's speed by using the known formula.
speed = distance traveled/time intervalWe are given that the runner ran a distance of 200m in a time of 35s. Let's substitute these values in the formula to find the runner's speed.
The runner's speed is 407, or approximately 5.71m/s.
Writing and Graphing the Inequality
Now that we know that speed≈ 5.71m/s, we can write an inequality that represents any speed faster than the runner's speed. Note that the runner's speed is not included in the solution set.
r>5.71
Since this is a strict inequality, our graph will be an open circle on the runner's speed extending out in the positive direction.
b In order to decide whether every point in the inequality could represent the speed of a runner, let's look Usain Bolt's world record for the 200meter dash that he set in 2009 as a point of perspective. We will need to use the formula for the speed once again.
speed = distance traveled/time interval
If we substitute Bolt's distance 200m and time 19.19s into the formula, we find that his world-record speed was r≈10.4m/s. Let's plot this on our inequality graph from above.
Since the inequality continues on into infinity, beyond even Usain Bolt's world record, we cannot say that every point in our inequality could represent the speed of a runner.
