# Calculating Average Speed: Physics Homework Problem

• dyavol33
In summary, the conversation discusses a problem in a physics class involving finding the average speed of a road trip with two different speeds for different parts of the trip. The individual asks for help in finding the time it takes to travel each part and how to calculate the average speed for the entire trip. Through the conversation, it is determined that the equations for average speed, distance, and time are needed and a proportion can be set up to find the missing time. A final answer of 54.9 km/hr is calculated.
dyavol33

## Homework Statement

So here's a problem I need help with for my physics class that's due tomorrow night.

On a road trip, a driver achieved an average speed of 76 km/h for the first 86.0 km and an average speed of 38 km/h for the remaining 54.0 km. What was her average speed (in km/h) for the entire trip? Round your final answer to three significant figures.

## Homework Equations

Umm... see next part?

## The Attempt at a Solution

So I know that the first thing I have to do is find how long it takes for the driver to drive the first and second parts of the road trip using the average speed given for each part. But I'm not exactly sure how to do it. For the first part, do I divide 76 km/h by 60 minutes to get how far they travel in 1 minute? Then times it by how far they traveled?
So it would be 76/60=1.267, then 1.267*86=109? Am I somewhat doing this right? Any help would be greatly appreciated!

dyavol33 said:
So I know that the first thing I have to do is find how long it takes for the driver to drive the first and second parts of the road trip using the average speed given for each part.
Good insight.
For the first part, do I divide 76 km/h by 60 minutes to get how far they travel in 1 minute? Then times it by how far they traveled?
There is no need to involve minutes at all. No measurements in the problem use minutes. How many hours does it take to go 86 km at 76 km/hour?

dyavol33 said:
do I divide 76 km/h by 60 minutes to get how far they travel in 1 minute?
What equation relates average speed, distance and time? (This is what you should have written under Relevant Equations in the template.)
Rearrange it into the form time = ...

haruspex said:
What equation relates average speed, distance and time? (This is what you should have written under Relevant Equations in the template.)
Rearrange it into the form time = ...
I know speed=distance/time
So time=distance/speed

jbriggs444 said:
Good insight.

There is no need to involve minutes at all. No measurements in the problem use minutes. How many hours does it take to go 86 km at 76 km/hour?
This is where I get stumped. I know it takes one hour to travel 76 km, but I don't know how to calculate how long it will take to travel the extra 10 km to get to 86 km. I know it's probably really simple, but I just don't know how to figure it out.

dyavol33 said:
This is where I get stumped. I know it takes one hour to travel 76 km, but I don't know how to calculate how long it will take to travel the extra 10 km to get to 86 km. I know it's probably really simple, but I just don't know how to figure it out.
You can find this time by setting up a proportion.
At a fixed rate: the distance traveled is directly proportional to the time of travel.

dyavol33 said:
I know speed=distance/time
So time=distance/speed
Right. Apply that.

SammyS said:
You can find this time by setting up a proportion.
At a fixed rate: the distance traveled is directly proportional to the time of travel.
Thank you! I think what you said was what I needed to figure out this problem.
So do I have this right:
76 km/h = 54 km/x, which you cross multiply
so x=1.13, which means it took 1.13 hrs to drive the first part of the trip
Then 38km/hr = 54km/x
which makes x = 1.42
So it took 1.42 hours to drive the second half of the trip!

haruspex said:
Right. Apply that.
So I figured out the average speed of the parts of the trip, so I just need to figure out the average speed of the entire trip. So I just plug it into the equation:
Average Speed = Distance/Time = (86 km+54 km)/(1.13 hr+1.42 hr) = 54.9
So my final answer would be 54.9 km/hr!

dyavol33 said:
Thank you! I think what you said was what I needed to figure out this problem.
So do I have this right:
76 km/h = 54 km/x, which you cross multiply
so x=1.13, which means it took 1.13 hrs to drive the first part of the trip
Then 38km/hr = 54km/x
which makes x = 1.42
So it took 1.42 hours to drive the second half of the trip!
Those are correct except for a typo. It should be 76 km/h = (86 km)/x.

dyavol33 said:
So I figured out the average speed of the parts of the trip, so I just need to figure out the average speed of the entire trip. So I just plug it into the equation:
Average Speed = Distance/Time = (86 km+54 km)/(1.13 hr+1.42 hr) = 54.9
So my final answer would be 54.9 km/hr!
That looks good, but you should put units on the answer.

dyavol33 said:
So I figured out the average speed of the parts of the trip, so I just need to figure out the average speed of the entire trip. So I just plug it into the equation:
Average Speed = Distance/Time = (86 km+54 km)/(1.13 hr+1.42 hr) = 54.9
So my final answer would be 54.9 km/hr!
Yes.

SammyS said:
Those are correct except for a typo. It should be 76 km/h = (86 km)/x.

That looks good, but you should put units on the answer.
Oops, I didn't notice that typo. I had it written correctly on my paper, but typed it in wrong here

Awesome, thank you everyone for the help!

dyavol33 said:
Oops, I didn't notice that typo. I had it written correctly on my paper, but typed it in wrong here
Yes. I could tell by the answer you gave that you must have used 86 and not the 54 that was written.

## 1. What is average speed?

Average speed is a measure of how fast an object travels in a given amount 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 considers the total distance traveled and the total time taken, while instantaneous speed is the speed at a specific moment in time. Average speed gives an overall picture of how fast an object is moving, while instantaneous speed can vary.

## 3. Can average speed be negative?

Yes, average speed can be negative if the object travels in the opposite direction of the positive direction. For example, if a car travels east for 5 miles and then turns around and travels west for 3 miles, its average speed would be -2 miles per hour.

## 4. How is average speed different from average velocity?

Average speed is a measure of how fast an object travels, while average velocity is a measure of how fast and in what direction an object travels. Average velocity takes into account the displacement of an object, while average speed does not.

## 5. Can an object have the same average speed but different average velocities?

Yes, an object can have the same average speed but different average velocities if it travels the same distance in different directions. For example, if a car travels 100 miles north and then 100 miles south, its average speed would be the same in both cases, but the average velocity would be different since it traveled in opposite directions.

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