A relay team is going to participate in a 150-mile bicycle race. One rider averages 12 miles per hour. The second averages 16 miles per hour. Write a function modeling their trip, where x = the hours ridden by the first bicyclist and y = the hours ridden by the second bicyclist.
12x + 16y = 150
To write a function modeling the trip of the relay team, we need to consider the distances covered by each rider and the total distance of the race.
Let's break down the problem and compute the distances covered by both the first and second riders.
The first rider averages 12 miles per hour, so the distance covered by the first rider can be represented as:
Distance covered by the first rider = 12 * x.
Similarly, the second rider averages 16 miles per hour, so the distance covered by the second rider can be represented as:
Distance covered by the second rider = 16 * y.
Since the total distance of the race is given as 150 miles, the sum of the distances covered by both riders should equal the total distance:
12 * x + 16 * y = 150.
Therefore, the function modeling their trip can be written as:
f(x, y) = 12 * x + 16 * y - 150.
This function will give us the difference between the total distance covered by both riders and the actual distance of the race. If this difference is zero, it means the riders have completed the full distance of the race.
Note that this function assumes that both riders start at the same time. If there are any delays or gaps between their start times, the function would need to be adjusted accordingly.