SOLUTION: word problem probably a proportion d=rt I am stuck setting it up. As part of an exercise regimen, you walk 2 miles on an indoor track. Then you jog twice your walking speed for

Question 764384: word problem probably a proportion d=rt I am stuck setting it up.
As part of an exercise regimen, you walk 2 miles on an indoor track. Then you jog twice your walking speed for another 2 miles. If the total time spent walking and jogging is 1 hour, find the walking and jogging rates.
Found 2 solutions by stanbon, DrBeeee:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
As part of an exercise regimen, you walk 2 miles on an indoor track. Then you jog twice your walking speed for another 2 miles. If the total time spent walking and jogging is 1 hour, find the walking and jogging rates.
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Walk DATA:
distance = 2 miles ; rate = x mph ; time = 2/x hrs
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Jog DATA:
distance = 2 miles ; rate = 2x mph ; time = 2/(2x) = 1/x hrs
------
Equation:
time + time = 1 hr
---
2/x + 1/x = 1
2 + 1 = x
x = 3 mph (Walking rate)
2x = 6 mph (Jogging rate)
==========================
Cheers,
Stan H.
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Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
I like to use a chart for distance problems but can't draw one here. I'll try to explain it to you.
First you need to know the basic formula for distance travelled is given by
(1) d = r*t, that is d is the distance in miles, r is the rate of speed in miles per hour and t is the time travelled at that speed in hours.
In your problem we know the distance, 2 miles for each "leg", one leg for walking and one leg for jogging. So we need to know the time it takes to cover each leg. Time is given by
(2) t = d/r where we see that time is a function of the rate.
For the first leg (walking), let the rate be w, and the time of walking be Tw, then we have
(3) Tw = d/w or
(4) Tw = 2/w
Now for the jogging leg the distance is also 2 miles, but the rate is twice that of walking or 2*w, so letting Tj represent the time for jogging we have
(5) Tj = 2/(2*w) or
(6) Tj = 1/w
We need one more piece of information to solve the problem. This the fact that the total time of the two legs takes one hour, so we have that the sum of Tw and Tj is one hour or
(7) Tw + Tj = 1
Now put (4) and (6) into (7) and get
(8) 2/w + 1/w = 1
Now multiply both sides of (8) by w to get
(9) 2 + 1 = w or
(10) w = 3
That is we walk at 3mph and jog at 2*3 or 6mph.
Let's check this using (3), (4) and (7)
Is (2/3 + 2/6 = 1)?
Is (4/6 + 2/6 - 1)?
Is (6/6 = 1)?
Is (1 = 1)? Yes
Comment: In general, problem solving uses the same steps.
A. List of Knowns
B. List of Unknowns
C. Define variable to represent all of the unknowns
D. Define the controlling Formula of the problem (d = rt here)
E. (Tough part) Now write a sufficient number of equations to solve the problem
F. Solve the equations
G. Check your answers
H. Answer the question.
.
.
Apply this to your problem: How many equation/relationships do you need to solve your travel problem and how did we use them?
a) we have two legs governed by the formula d = rt.
b) to solve the formula for any one of the 3 unknowns d,r,t we need to know the other two.
c) so we need info on 2*2 = 4 variables in order to solve our problem
d) we used distance = 2 and distance = 2 (two relationships)
d) we used rate of jogging was twice walking rate (one relationship)
e) we used total time of one hour (one relationship)
We combined these four relationships in the basic formula t = d/r to get our answer.

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