Word Problem Help

Question

During strenuous exercise a certain athlete can burn 9 calories per minute on a stationary bicycle and 14.5 calories per minute on a stair climber. In a 30 minute workout the athlete burns 347 calories. How many minutes does the athlete spend on each type of exercise equipment?

Answer 1

I would solve this with a matrix.

 

First, let x = minutes spent on the stationary bicycle

             y = minutes spent on the stair climber

 

Next, take what's know - and make it into equations:

 

(1)  Total minutes spent on both exercises:  30.  So:  x + y = 30

(2)  Stationary bicycle burns 9 calories; stair climber burns 14.5 calories; total of 347 calories burned; so:  
       9x + 14.5y = 347

 

This gives us what we need for the initial tableau, for Iteration 0:

 

1          1          =          30

9       14.5        =         347

 

We want to get the value for 1x and 1y; so, we get the value in R2,C1 to become 0; which gives us the row operation of:  -9R1 + R2 = new R2; which gives us the Iteration 1 matrix of:

 

1          1          =          30

0         5.5        =          77

 

Next, we want to get the value in R1,C2, to become 0;which gives us the row operation of: -2R2 + 11R1 = new R1; which gives us the Iteration 2 matrix of:

 

11         0          =          176

0           5.5       =           77

 

Next, we want to do row reductions, to get 1x = and 1y =; so:

 

(1/11)R1 = new R1

(1/5.5)R2 = new R2

 

This gives us the final matrix of:

 

1         0          =           16

0         1          =           14

 

This gives us (x,y) of (16,14); which means:

 

16 minutes on the stationary bicycle

14 minutes on the stair climber

 

To check our work, we plug these values into the 2 initial equations:

 

(1)  16 + 14 = 30     [Check]

(2)  9 * 16 + 14 * 14.5 = 347     [Check]