Use the formula D=rt where D is distance, r is rate, and t is time.
40 yard dash: Julio took 4.39 seconds, Rich took 6.18
1. Solve D=rt for rate. (1 pt)
40
2. Use the statistics given in Act Two and your equation from #1.
a. At what speed (rate) does Rich run the 40-yard dash? (1 pt)
b. At what speed (rate) does Julio run the 40-yard dash? (1 pt)
c. Solve D=rt for time. How long does it take Rich to run with a 10-yard lead? (1 pt)
D=30 yds
d. How long does it take Julio to run the 40-yard dash at half-speed? Who will win? (2 pts)
3. If both runners are at full speed, how many yards of a head start will Rich need to win? (2 pts)
4. Write and solve your own question using this scenario. (Remember to show all work!) (2 pts)
Still no ideas at all?
What about the formula confuses you?
D = rt, so
r = D/t
...
When you actually sit down and do the work it becomes confusing
1. To solve D=rt for rate (r), divide both sides of the equation by t: r = D/t.
2. a. To find the rate at which Rich runs the 40-yard dash, we need to substitute the given values into the formula. Given D = 40 yards and t = 6.18 seconds, we can use the equation r = D/t:
r = 40 yards / 6.18 seconds ≈ 6.47 yards/second.
b. To find the rate at which Julio runs the 40-yard dash, we substitute the given values into the formula. Given D = 40 yards and t = 4.39 seconds:
r = 40 yards / 4.39 seconds ≈ 9.11 yards/second.
c. To solve D=rt for time (t), divide both sides of the equation by r: t = D/r. Given D = 30 yards and r = 6.47 yards/second, we can plug in these values and solve for t:
t = 30 yards / 6.47 yards/second ≈ 4.63 seconds.
d. To find out how long it takes Julio to run the 40-yard dash at half-speed, we need to divide the rate by 2 (since half the speed means half the rate). Given D = 40 yards and r = 9.11 yards/second, we can calculate t using the equation t = D/r:
t = 40 yards / (9.11 yards/second / 2) ≈ 8.78 seconds.
Comparing this with the actual time it took Julio (4.39 seconds), we can see that it will take him longer at half-speed. Therefore, Rich will win the race.
3. If both runners are at full speed, we can calculate how many yards of a head start Rich needs to win. Given that Rich's rate is 6.47 yards/second and Julio's rate is 9.11 yards/second, we can set up the equation D = rt to represent the distance both runners will run:
40 yards + D = 6.47 yards/second * t
D = 9.11 yards/second * t
Since we know that t is the same for both runners, we can set the two equations equal to each other and solve for D:
6.47 yards/second * t = 9.11 yards/second * t
0 = 2.64 yards/second * t
To ensure that Rich wins, he needs a head start of at least 2.64 yards.
4. Write and solve your own question using this scenario:
Suppose Rich and Julio decide to run a longer race, this time covering a distance of 100 yards. Given that Rich's rate is 6.47 yards/second and Julio's rate is 9.11 yards/second, we can determine who wins the race.
We can use the formula D = rt to calculate how long it will take each runner to complete the race.
For Rich:
D = 100 yards
r = 6.47 yards/second
t = D/r
t = 100 yards / 6.47 yards/second ≈ 15.46 seconds
For Julio:
D = 100 yards
r = 9.11 yards/second
t = D/r
t = 100 yards / 9.11 yards/second ≈ 10.96 seconds
Comparing the times, we can see that Julio finishes the 100-yard race in a shorter time than Rich. Therefore, Julio would win the race.