Distance/rate Problem...having a brain cramp!

[jbecker007]

The problem:

A driver sets out on a 20-mile trip. When he has gone halfway, he finds he has averaged 25 mph. At what speed must he travel the rest of the way to make his overall average speed for the trip 40 mph?

I'm having trouble figuring out how to start this. He travels 10 miles at 25 miles per hour, which takes him 2/5 of an hour (24 minutes). Not sure if the time is relevant. I tried setting up an equation: r₁ + r₂ = 40, but this doesn't seem to be working either.

Any help would be deeply appreciated!

JB

 

[MarkFL]

Hello, and welcome to FMH!

If he is to travel 20 miles and at average speed of 40 mph, how long should the entire trip take him?

 

[jbecker007]

Hello, and welcome to FMH!

If he is to travel 20 miles and at average speed of 40 mph, how long should the entire trip take him?

30 minutes...so does that mean he has to make the last ten miles of the trip in 6 minutes?

 

[MarkFL]

30 minutes...so does that mean he has to make the last ten miles of the trip in 6 minutes?

Yes it does. How fast must he go to cover 10 miles in 6 minutes?

 

[jbecker007]

100 mph? I thought that might be the answer, but it seemed a little insane.

 

[MarkFL]

Yes, that's what I get as well.

 

[jbecker007]

Thank you!

 

[HallsofIvy]

Don't expect to math problems to be sane!

 

[MarkFL]

Yes, had the guy averaged 20 mph for the first 10 miles, he'd need a warp drive capable of warp 10 to fulfill the required average for the entire trip.

 

[harpazo]

Hello, and welcome to FMH!

If he is to travel 20 miles and at average speed of 40 mph, how long should the entire trip take him?

D = rt

20 = 40t

20/40 = t

1/2 = t

 

[HallsofIvy]

If I were your teacher I would deduct points for not answering "1/2 hour".

There were no "D" or "r" or "t" in the original statement of the problem. Your first line should have been "D= rt where D is the distance traveled in miles, r is the speed in miles per hour, and t is the time in hours".

 

[Steven G]

The problem:

A driver sets out on a 20-mile trip. When he has gone halfway, he finds he has averaged 25 mph. At what speed must he travel the rest of the way to make his overall average speed for the trip 40 mph?

I'm having trouble figuring out how to start this. He travels 10 miles at 25 miles per hour, which takes him 2/5 of an hour (24 minutes). Not sure if the time is relevant. I tried setting up an equation: r₁ + r₂ = 40, but this doesn't seem to be working either.

Any help would be deeply appreciated!

JB

Note that if r₁=25 and r₁+r₂ = 40, then r₂=15. If both speeds are less than 40mph then the average certainly could not be 40mph.