SOLUTION: 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 .05 mile per minute and

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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 .05 mile per minute and       Log On

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Question 253518: 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 .05 mile per minute and jog .1 mile per minute. For how much time were you walking? For how much time were you jogging?
I set it up as:
(((x+y=2.5)))
(((.05x+.1y=30)))
But it is not working out. Can you help me?
Found 2 solutions by solver91311, harshachittar:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Yes, I can.

Remember that distance equals rate times time, or .

But that means that time is equal to distance divided by rate, or

With that in mind, let's take a look at your second equation. The right hand side of your equation is 30, which I take to mean the given 30 minutes. That is an amount of time. Therefore, the left hand side of your equation should be the sum of two amounts of time, namely the amount of time spent walking plus the amount of time spent jogging. You have multiplied the walking rate (0.05) times the distance walked () and the jogging rate (0.1) times the distance jogged (). You should be dividing the distance by the rate, thus:



Now solve the system using your correctly constructed first equation. Write back if you need more help.

John

Answer by harshachittar(3) About Me  (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