Question

Given the number of calories expended by people with different weights and using different ways of exercising for 20 minute time periods is 120b 150lb 107 136]Bicycling A126 130Jogging 74 85] Walking A 120-pound person and a 150-pound person both bicycle for 40 minutes, jog for 10 minutes, and walk for 60 minutes.

Answer 1

Answer:

The 120-pound person expended 499 lb and the 150-pound person expended 592 lb.

Step-by-step explanation:

The matrix for number of calories expended by people with different weights and using different ways of exercising for 20 minute time periods is:

$X=\left[\begin{array}{cc}107&136\\126&130\\74&85\end{array}\right]$

It is provided that a 120-pound person and a 150-pound person both bicycle for 40 minutes, jog for 10 minutes, and walk for 60 minutes.

Then the matrix for the number of times the exercises are done is:

$Y=\left[\begin{array}{ccc}\frac{40}{20}&\frac{10}{20}&\frac{60}{20}\\\\\frac{40}{20}&\frac{10}{20}&\frac{60}{20}\end{array}\right] =\left[\begin{array}{ccc}2&0.5&3\\2&0.5&3\end{array}\right]$

Compute the number of calories expended by a 120-pound person and a 150-pound person as follows:

$YX=\left[\begin{array}{ccc}2&0.5&3\\2&0.5&3\end{array}\right]\times \left[\begin{array}{cc}107&136\\126&130\\74&85\end{array}\right]$

      $=\left[\begin{array}{ccc}(2\cdot107+0.5\cdot 126+3\cdot74)&(2\cdot136+0.5\cdot 130+3\cdot85)\\(2\cdot107+0.5\cdot 126+3\cdot74)&(2\cdot136+0.5\cdot 130+3\cdot85)\end{array}\right]$

      $=\left[\begin{array}{ccc}499&592\\499&592\end{array}\right]$

Thus, the 120-pound person expended 499 lb and the 150-pound person expended 592 lb.