I'll help you get started. Let the distance each has to run be "x", the distance each has to swim "y", and the distance each has to cycle "z", all in miles, of course.
Velocity has units of mi/hr because it is "distance (mi.) divided by time (hr.)", v= d/t. Multiplying on both sides by t, vt= d. Dividing on both sides by v, t= d/v. I did that because this problem tells us velocities and I have assigned labels to the distances. I have those together on the right side of the equation.
Look at Amanda only, she ran a distance x miles at 10 mi/hr so took x/10 hours. She swam a distance y miles at 4 mi/hr so took y/4 hours. She cycled a distance z miles at 20 mi/hr so took z/20 hr. She took a total x/10+ y/4+ z/20 hours. The problem tells us she took 2 hours and 30 minutes which is 2.5 hours.
The equation is x/10+ y/4+ z/20= 2.5. If you don't like fractions (I don't!) multiply both sides by 20: 2x+ 5y+ z= 50.
Now you finish!