Solving Matrix Word Problem: Amanda, Bryce & Corey

[wat2000]

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)
amandas time 10 running, 4 swimming, and 20 cycling
Bryce 7.5, 6,and 15
corey 15, 3,40a. write the system of equations

b.set up the matrix equations AX=B and solve it

x/10 + y/4 + z/20 = 105/60
x/7.5 + y/6 + z/15 = 150/60
x/15 + y/3 + z/40 = 180/60

is this close?

 

[wat2000]

Matrix word aplication problem

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 cyclinga. write the system of equations

b.set up the matrix equations AX=B and solve it

x/10 + y/4 + z/20 = 105/60
x/7.5 + y/6 + z/15 = 150/60
x/15 + y/3 + z/40 = 180/60

is this close? The answers in my book are 5 mile swim,2 mile swim,and 30 mile cycle. I can't get it though.

 

[Dustinsfl]

Are those times for running, swimming, and biking minutes per mile?

Also, if Corey finished in 1:45, that is 60 minutes + 45 minutes.

[tex]1+\frac{45}{60}=\frac{7}{4}[/itex]

 

[wat2000]

Its their average speeds.

 

[Dustinsfl]

Its their average speeds.

Avg speed per mile?

 

[wat2000]

yes i reworded it. My book says the answer is 5 mile run, 2 mile swim and 30 mile cycle. I think i could get this on my calculator using the matrix function if i could just get it set up right

 

[wat2000]

This must not be the right way to set it up because I am not getting 5, 2 or 30. i need to know what it lokks like in matrix form.

 

[eumyang]

I'm not sure where you are getting the numbers on the right side. Assuming that the speeds are in mph, I would think the system would be this (corrections in bold), with the participants' total time on the right hand side (in hours):

x/10 + y/4 + z/20 = 2.5
x/7.5 + y/6 + z/15 = 3
x/15 + y/3 + z/40 = 1.75

 

[wat2000]

I tried to do it like that and when i put it in my calculator to find the inverse matrix it didnt give me the 5 2 and 30 i needed. do you know what i did wrong? I see what you mean about the numbers. i must of typed them wrong. i went back and edited it. i still can't get the right answer though.

 

[Mark44]

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 up the matrix equations AX=B and solve it

x/10 + y/4 + z/20 = 105/60
x/7.5 + y/6 + z/15 = 150/60
x/15 + y/3 + z/40 = 180/60

is this close?

Yes, it's close, but the numbers on the right sides aren't right.
x/10 + y/4 + z/20 = 2.5
x/7.5 + y/6 + z/15 = 3
x/15 + y/3 + z/40 = 1.75

The first equation represents Amanda's time of 2.5 hours; the second equation represents Bryce's time of 3 hours; the third equation represents Corey's time of 1.75 hours.

To solve this system, multiply through each equation to clear fractions, and then row reduce the matrix.

The answers in my book are 5 mile swim,2 mile swim,and 30 mile cycle. I can't get it though.

 

[Mark44]

Are those times for running, swimming, and biking minutes per mile?

No, only one time is given for each participant. The other numbers are their speeds for each leg of the triathlon.

Avg speed per mile?

?
A number in the table represents that person's speed for a particular leg of the event. For example, the 10 in the upper left corner means that Amanda's speed (average) for the running portion was 10 mph.

 

[eumyang]

Strange. I was able to get the answer after typing in matrices A (consisting of the coefficients on the left side) and B (consisting of the numbers on the right side) and calculating A^-1B. Can you show us what you typed in as your matrices A and B?

 

[HallsofIvy]

This problem was also posted in the "Calculus and Beyond Homework" section. I am merging the two.