Question

myra is training for a triathlon and needs to swim a certain distance for todays workout. if she swims at the rec center pool, she will complete a 250-yard warmup and then swim laps in a lane that is 50 yards long. if myra swims at the indoor pool at her gym, she will complete a 300-yard warmup, plus a main set that consists of 40 yards per lap. if myra swims the correct number of laps, she can complete the same distance in either pool. how long will myras workout be in total?
write a system of equations, graph them, and type the solution.
graph with y-axis labeled distance (0 - 500) and x-axis labeled laps (0 - 10), and two buttons: rec center (orange) and gym (blue)

Explanation:

Step1: Define variables and write equations

Let \( x \) be the number of laps and \( y \) be the total distance. For the rec center: \( y = 50x + 250 \). For the gym: \( y = 40x + 300 \).

Step2: Solve the system of equations

Set \( 50x + 250 = 40x + 300 \). Subtract \( 40x \) and \( 250 \): \( 10x = 50 \), so \( x = 5 \).

Step3: Find total distance

Substitute \( x = 5 \) into either equation. Using rec center: \( y = 50(5) + 250 = 250 + 250 = 500 \).

Answer:

The total distance of Myra's workout is 500 yards.