I can't figure out this math equation. I know what the answer is but not how to solve it.?

Question

As part of an exercise regimen, you walk 2 miles on an indoor track. Then you jog at twice your walking speed for another 2miles. If the total time spent walking and jogging is 1 hour, find the walking and jogging rates. PLEASE HELP!!!

Answer 1

Time = distance / speed

Walking speed = v
Jogging speed = 2v

2/v + 2/(2v) = 1
4/(2v) + 2/(2v) = 1
6/(2v) = 1
2v = 6
v = 3 mph
2v = 6mph

Walking speed: 3mph
Jogging speed: 6mph

Answer 2

Say that W is your walking speed so the time to go 2 miles is 2/W [distance of 2 miles divided by speed W].
Then 2 x W is your jogging speed so the time to go 2 miles is 2/(2 x W) = = 1/W [distance of 2 miles divided by speed of 2 x W].

The total time from both walking and jogging is 2/W + 1/W = 1 and that is the equation to solve.

Multiply both sides by W to separate the variables and the constants.

That gives you 2 + 1 = W which means that W is = 3 miles per hour walking. Since jogging is twice as fast as walking then jogging is 6 miles per hour.

Answer 3

This is a little tricky - but it works!

If you walk and jog for a total of 1 hour and your jog speed is twice your walk speed, walking time will be twice your jogging time.

Step 1 - Time walking 2x; Time running x

2x +x =60minutes
3x =60 minutes
x=20minutes

You spend 40 minutes walking and 20 minutes jogging.


Now let x be walking speed in mph and 2x be jogging speed

40 minutes x/60 minutes + 20 minutes 2x/60minutes = 4 miles

2/3 x + 2/3 x = 4miles
4/3 x = 4 miles
x = 3miles

So you are walking at 3 miles per hour
and you are running at 6 miles per hour.

Check

3mph * 2/3 hour + 6mph * 1/3 hr = 4 miles?
2 miles + 2 miles = 4miles?
4 miles = 4miles YES!!!

Hope this helps.

Answer 4

You spend half as much time jogging as walking.
Therefore, let 2t = time spent walking and t = time spent jogging in hours. So then you have 2t + t = 3t = 1 hour since you spent a total of 1 hour walking and jogging.

Thus t = 1/3 hour.

Then, using speed = distance/time:

Walking speed = 2 mi / (2/3 h) = 3 mph

Jogging speed = 2 mi / (1/3 h) = 6 mph

Answer 5

hour = t1 + t2
hour = 2miles/Rw + 2miles/(2Rw)
hour/miles = 2/Rw(1+(1/2))
hour/miles = 3/Rw

3miles/hour = Rw