as a part of an exercise regimen, you walk 8 miles..

Question

as apart of an exercise regimen, you walk 8 miles on an indoor track. then you jog at twice your walking speed for another 8 miles.ifthe total time spent walking and jogging is 3 hours, what are the walking and jogging rates?

Answer 1

Hi Elizabeth, this problem is an application of the D(istance) = R(ate) * T(ime) formula. Let x be the rate you walk, then 2x will be the rate you jog. Your total time walking and jogging is 3 hours.

 

Set up equation:

 

Let T_w be the time walking.

 

Let T_j be the time jogging.

 

T_w + T_j = 3

 

D = R * T_w, or T_w  = D / R

 

D = 2R * T_j, T_j = D / 2R

 

Substitute for T_w and T_j:

 

Note: D is 8 miles, for both walking and jogging:

 

8 / R + 8 / 2R = 3

 

Clear the fractions by multiplying all terms by 2R

 

2R( 8 / R + 8 / 2R = 3)

 

16 + 8 = 6R

 

24 = 6R

 

Divide both sides by 6:

 

R = 4

 

The rate you walked at was 4 miles per hour. The rate you jogged at was 2 * 4, or 8 miles per hour.

 

Questions?