# Did I approach this problem correctly?

1. Jan 16, 2014

### emlekarc

If you are going on a long trip is there a difference between going half the distance at 45mi/h and the other half at 50mi/hour, compared to going half the time at 45mi/h and the other half at 50mi/h?

So wouldn't the first part be:
(95)/60?
The second part would be:
(95)/30

Or would it be:
(45/60)+(50/60) for the first part and (95)/60 fht the second?

Last edited: Jan 16, 2014
2. Jan 16, 2014

### Staff: Mentor

3. Jan 16, 2014

### MostlyHarmless

There are the same.

4. Jan 16, 2014

### emlekarc

The first part, I added up the distances (45+50) and divided it by the time (60 minutes).
The second part, I added up the distance again, but took it out of 30 since it says you are spending half the time (30 minutes) at each speed?

5. Jan 16, 2014

### Staff: Mentor

The problem statement doesn't mention any particular time or distance for the entire trip. It only gives you the speeds. You'll have to represent the total distance as some unknown, say "D", and assume that this total distance is the same for both cases.

In one case the total distance is divided in two and you travel the first half of the total distance at one speed and the second half at the other speed. In the second case it's the time that divided in half so you travel at one speed for half the time, the other speed for the other half of the time. The total time to complete the trip in each case is not necessarily the same...

I suggest that you try to determine the average velocity for each case.

6. Jan 17, 2014

### lightgrav

this is a conceptual question, so it would be better to use more extreme values; say 20 mph and 60 mph.
If you go 20 mph for an hour and then 60 mph for an hour, how far do you get?
If someone else goes 20 mph for 40 miles, how long would that take? How long to go the other 40 miles at 60 mph?

7. Jan 17, 2014

### Staff: Mentor

As follow up to Gneill's response in #5, split this up into two separate problems to find the average velocity in each case.

Problem 1: Let 2D be the total distance covered, and let D be the distance covered at 45 mph and let D be the distance covered at 50 mph. In terms of D, how much time does it take to cover D at 45 mph? In terms of D, how much time does it take to cover D at 50 mph? In terms of D, what is the total amount of time to cover the distance 2D? What is the average velocity?

Problem 2: Let T be the amount of time traveled at 45 mph, and let T be the amount of time traveled at 50 mph. In terms of T, how much distance is covered at 45 mph? In terms of T, how much distance is covered at 50 mph? What is the total distance covered over the total time interval 2T? what is the average velocity?