Amanda, Bryce, and Corey enter a race in whic they have to run, swin, and cycle over a marked course. Their average speeds are given in the table below. Corey finishes first with a total time of 1h 45min. Amanda comes in second with a time of 2h 3min. Bryce finishes last with a time of 2h. Find the distance (in miles) for each part of the race.
Amanda:
Running - 10 (mi/h)
swimming - 4 (mi/h)
cycling - 20 (mi/h)
Bryce:
Running - 7 1/2 (mi/h)
swimming - 6 (mi/h)
cycling - 15 (mi/h)
Corey:
Running - 115 (mi/h)
swimming - 3 (mi/h)
cycling - 40 (mi/h)
To find the distance of each part of the race, we can use the formula distance = speed * time.
Let's start by finding Corey's distance for each part of the race.
For running, Corey's speed is 115 mi/h and his total time is 1 hour and 45 minutes, which is 1.75 hours. So, the distance Corey ran is 115 mi/h * 1.75 h = 201.25 miles.
For swimming, Corey's speed is 3 mi/h and his total time is 1.75 hours. So, the distance Corey swam is 3 mi/h * 1.75 h = 5.25 miles.
For cycling, Corey's speed is 40 mi/h and his total time is 1.75 hours. So, the distance Corey cycled is 40 mi/h * 1.75 h = 70 miles.
Now, let's find Amanda's distance for each part of the race.
For running, Amanda's speed is 10 mi/h and her total time is 2 hours and 3 minutes, which is 2.05 hours. So, the distance Amanda ran is 10 mi/h * 2.05 h = 20.5 miles.
For swimming, Amanda's speed is 4 mi/h and her total time is 2.05 hours. So, the distance Amanda swam is 4 mi/h * 2.05 h = 8.2 miles.
For cycling, Amanda's speed is 20 mi/h and her total time is 2.05 hours. So, the distance Amanda cycled is 20 mi/h * 2.05 h = 41 miles.
Lastly, let's find Bryce's distance for each part of the race.
For running, Bryce's speed is 7.5 mi/h and his total time is 2 hours. So, the distance Bryce ran is 7.5 mi/h * 2 h = 15 miles.
For swimming, Bryce's speed is 6 mi/h and his total time is 2 hours. So, the distance Bryce swam is 6 mi/h * 2 h = 12 miles.
For cycling, Bryce's speed is 15 mi/h and his total time is 2 hours. So, the distance Bryce cycled is 15 mi/h * 2 h = 30 miles.
Therefore, the distances for each part of the race are as follows:
Corey:
Running - 201.25 miles
Swimming - 5.25 miles
Cycling - 70 miles
Amanda:
Running - 20.5 miles
Swimming - 8.2 miles
Cycling - 41 miles
Bryce:
Running - 15 miles
Swimming - 12 miles
Cycling - 30 miles