Question

Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a 12.4-mile bike ride, and a 3.1-mile run. a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her ave swimming speed in miles per minute? b. What is her average swimming speed in miles per hour?

c. Write an equation relating the total distance Yu Yan swims d in miles to the number of minutes she swims m.
d. Write an equation relating the total distance Yu Yan swims d in miles to the number of hou she swims h.
e. Part of the swim portion of the race involves swimming the full length of a pier, which is 0.2 miles long. Yu Yan swims at her average speed. How many minutes does it take Yu Yar to reach the end of the pier?
f. Yu Yan completes the bike ride in 48 minutes. What is her average biking speed in miles per hour?
g. Write an equation relating the total distance Yu Yan bikes a to the time in hours she bikes h.

Answer 1

a. Yu Yan's average swimming speed is 0.02 miles per minute and her average swimming speed is 1.2 miles per hou. c. The equation relating the total distance Yu Yan swims (d) in miles to the number of minutes she swims (m) is d = 0.02m. d. The equation relating the total distance Yu Yan swims (d) in miles to the number of hours she swims (h) is d = 1.2h. e. Yu Yan takes 10 minutes to reach the end of the pier. f. Yu Yan's average biking speed is 15.5 miles per hour. g. The equation relating the total distance Yu Yan bikes (a) to the time in hours she bikes (h) is a = 15.5h.

Step-by-step explanation:

a. To find Yu Yan's average swimming speed in miles per minute, we divide the total distance she swims (0.5 miles) by the time it takes her to swim (25 minutes). So, her average swimming speed is 0.5 miles / 25 minutes = 0.02 miles per minute.

b. To find Yu Yan's average swimming speed in miles per hour, we first convert her time from minutes to hours by dividing by 60 (25 minutes / 60 minutes per hour). Then, we divide the total distance she swims (0.5 miles) by the time it takes her to swim in hours. So, her average swimming speed is 0.5 miles / (25 minutes / 60 minutes per hour) = 1.2 miles per hour.

c. The equation relating the total distance Yu Yan swims (d) in miles to the number of minutes she swims (m) is d = 0.02m.

d. The equation relating the total distance Yu Yan swims (d) in miles to the number of hours she swims (h) is d = 1.2h.

e. If the length of the pier is 0.2 miles and Yu Yan swims at her average speed, we can use the equation from part c to find the time it takes her to reach the end of the pier. Plugging in the values, we get 0.2 miles = 0.02m. Solving for m, we find that it takes Yu Yan 10 minutes to reach the end of the pier.

f. To find Yu Yan's average biking speed in miles per hour, we divide the total distance she bikes (12.4 miles) by the time it takes her to bike (48 minutes). So, her average biking speed is 12.4 miles / 48 minutes = 0.2583 miles per minute. To convert this to miles per hour, we multiply by 60 (since there are 60 minutes in an hour). So, her average biking speed is 0.2583 miles per minute * 60 = 15.5 miles per hour.

g. The equation relating the total distance Yu Yan bikes (a) to the time in hours she bikes (h) is a = 15.5h.