Calculating Average Speed: Physics Homework Problem

[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!

 

[jbriggs444]

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?

 

[haruspex]

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 = ...

 

[dyavol33]

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

 

[dyavol33]

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.

 

[SammyS]

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.

 

[haruspex]

I know speed=distance/time
So time=distance/speed

Right. Apply that.

 

[dyavol33]

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!

 

[dyavol33]

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!

 

[SammyS]

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.

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.

 

[haruspex]

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.

 

[dyavol33]

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

 

[dyavol33]

Awesome, thank you everyone for the help!

 

[SammyS]

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.