Question 20748: Fitness Fitness For 30 minutes you do a combination of walking and jogging. At the end of your workout your pedometer displays a total of 2.5 miles. You know that you walk 0.05 mile per minute and jog 0.1 mile per minute. For how much time were you walking? For how much time were you jogging? Use a verbal model to write and solve a system of linear equations.
Found 2 solutions by kapilsinghi, harshachittar:
Answer by kapilsinghi(68)   (Show Source):
You can put this solution on YOUR website! Q: Fitness Fitness For 30 minutes you do a combination of walking and jogging. At the end of your workout your pedometer displays a total of 2.5 miles. You know that you walk 0.05 mile per minute and jog 0.1 mile per minute. For how much time were you walking? For how much time were you jogging? Use a verbal model to write and solve a system of linear equations.
Ans: Let Jogging Time be x minutes
so Walking Time is 30 - x Minutes
My Jogging Speed = 0.1 mile/minute
so Distance i jogged = 0.1*x
My Walking Speed = 0.05 mile/minute
so Distance i walked = 0.05*(30-x)
total distance covered = 2.5 Miles
So 0.1*x + 0.05*(30-x) = 2.5
0.1x + 1.5 - 0.05x = 2.5
0.05x = 2.5 - 1.5
0.05x = 1
x = 1/0.05
x = 20
So the time i spent jooging = x = 20 Minutes
and the time i spent walking = 30 - x = 10 Minutes
Kapil
Answer by harshachittar(3) (Show Source):
You can put this solution on YOUR website! Okay here goes,
Before I start the solution please notice that the time is in minutes but the distance is in miles/hr.
Information given,
Total Time, t = 30 mins or 1/2 hr or .5 hr
Total distance, d = 2.5 miles/hr
Rate of walking Rw = 0.05 miles/min or 3 miles/hr
Rate of jogging Rj = 0.1 miles/min or 6 miles/hr
To Find,
Time jogged, Tj = ?
Time walked, Tw = ?
Let Dj be the distance jogged and Dw be the distance walked
Dj + Dw = 2.5 ------------ Equ (1)
Tj + Tw = 0.5 ------------ Equ (2)
We know that
D = T x R
so,
Dw = Tw x Rw
Dj = Tj x Rj
Replace the above in Equ (1)
(Tw x Rw) + (Tj x Rj) = 2.5 -------------- Equ (3)
From Equ(2) we get,
Tw = 0.5 - Tj,
So Equ (3) becomes
[(0.5 - Tj) x 3] + (6 x Tj) = 2.5
Solving the above equation for Tj we get,
Tj = 1/3 hr
Since,
Tw + Tj = 1/2
Tw = 1/2 - 1/3
Tw = 1/6
Time spent walking is 1/6 hr or 10 mins
Time spent jogging is 1/3 hr or 20 mins
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