What is the Average Speed of a Car Traveling Up and Down Hills?

In summary, the problem involves a car traveling at two different speeds, 31 km/h and 59 km/h, up and down a hill. The task is to find the average speed for the round trip. Using the basic definition of average speed (total distance/total time), we can solve for the average speed by assuming the distance up the hill is equal to the distance down the hill. From there, we can calculate the time for each segment and find the average speed by dividing the total distance by the total time. The correct average speed is 40.667 km/h.
  • #1
mossfan563
54
0

Homework Statement


A car travels up a hill at 31 km/h and then down a hill at 59 km/h.
Find the avg speed.


Homework Equations





The Attempt at a Solution


I tried adding the speeds and then dividing by 2 but I guess that's definitely not how to approach this problem.

How do I go about starting this problem?
 
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  • #2
?? That's all you're given? I thought average speed was total dist/total time.
 
  • #3
Defennder said:
?? That's all you're given? I thought average speed was total dist/total time.

Yeah all I'm given is that those speeds are constant and they want the avg speed for the round trip.

Maybe "round trip" gives something away.
 
  • #4
Anybody?
 
  • #5
Assume the car travels x miles uphill and x miles downhill. Find the total time and divide 2x by the total time.
 
  • #6
mossfan563 said:

Homework Statement


A car travels up a hill at 31 km/h and then down a hill at 59 km/h.
Find the avg speed.
I presume that the distance up the hill equals the distance down the hill. (Without some such assumption, there would be insufficient information.)

What's the most basic definition of average speed? Use it.
 
  • #7
Ygggdrasil said:
Assume the car travels x miles uphill and x miles downhill. Find the total time and divide 2x by the total time.
Ok I get a really small number. Is that legit?

I assumed the car traveled 10 km up and down and i divided by 20 (2x).
I got .024603...
Is that correct? Or am I doing something wrong?
 
  • #8
Doc Al said:
I presume that the distance up the hill equals the distance down the hill. (Without some such assumption, there would be insufficient information.)

What's the most basic definition of average speed? Use it.

The basic definition is total distance/total time. I have no instance of time and no distance either.
 
  • #9
mossfan563 said:
The basic definition is total distance/total time.
Good.
I have no instance of time and no distance either.
Use Ygggdrasil's hint: Call the distance x (or D, if you like). In terms of the distance, find the time for going up and the time for going down.
 
  • #10
mossfan563 said:
Ok I get a really small number. Is that legit?

I assumed the car traveled 10 km up and down and i divided by 20 (2x).
I got .024603...
Is that correct? Or am I doing something wrong?

Check the units on your calculation. You'll see where your calculation went wrong.
 
  • #11
I see where i went wrong. I divided the other way around.
Does 40.666666666... sound right now?
 
  • #12
Yup. Of course, this assumes that the distance up the hill is equal to the distance down the hill, which may or may not be a correct assumption.
 
  • #13
It is correct. Thanks for the help!
 

Related to What is the Average Speed of a Car Traveling Up and Down Hills?

1. What is average speed?

Average speed is a measure of how fast an object is moving over a certain period of time. It is calculated by dividing the total distance traveled by the total time taken.

2. How is average speed different from instantaneous speed?

Average speed is the overall rate of motion over a period of time, while instantaneous speed is the speed at a specific moment in time. Average speed takes into account changes in speed, while instantaneous speed does not.

3. What are the units for average speed?

The units for average speed depend on the units used for distance and time. For example, if distance is measured in kilometers and time is measured in hours, then the units for average speed would be kilometers per hour (km/h).

4. Can average speed be negative?

Yes, average speed can be negative if the object is moving in the opposite direction of its initial velocity. For example, if a car is driving east at 50 km/h and then turns around and drives west at 25 km/h, its average speed for the entire trip would be -25 km/h.

5. What factors can affect the average speed of an object?

The average speed of an object can be affected by factors such as distance, time, acceleration, and external forces (such as friction or air resistance). Changing any of these factors can result in a change in average speed.

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