Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1 hours 45minutes, Amanda comes in second with a time of 2 hours 30 minutes, and Bryce finishes last with a time of 3 hours. Find the distance (in miles) for each part of the race.(hint: use the motion formula d=rt)
average speed(mi/h)
amanda: 10 running, 4 swimming, and 20 cycling
Bryce: 7.5 runnnig, 6swimming,and 15cycling
corey: 15 running, 3 swimming,40 cycling

a. write the system of equations

b.set

Question

Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1 hours 45minutes, Amanda comes in second with a time of 2 hours 30 minutes, and Bryce finishes last with a time of 3 hours. Find the distance (in miles) for each part of the race.(hint: use the motion formula d=rt)
average speed(mi/h)
amanda: 10 running, 4 swimming, and 20 cycling
Bryce: 7.5 runnnig, 6swimming,and 15cycling
corey: 15 running, 3 swimming,40 cycling

a. write the system of equations

b.set

anonymous · Answer

Let d1=distance for running,
d2=distance for swimming
d3=distance for cycling
corey => 15d1+3d2+40d3=1.75
amanda => 10d1+4d2+20d3=2.5
bryce => 7.5d1+6d2+15d3=3

anonymous · Answer

how would i set this up as a matrix? I know the answers are 5miles running 2 miles swimming and 30 miles cycling. but i dont know how to get that.