Second opinion needed at UAV Exercise

[Const@ntine]

Homework Statement

We're driving with a Uav of 80 km/h
The duration Δt is 2 h 45 min
On a rainy day, our Uav' is 65 km/h
If the distance is the same, how much more is the duration of the drive?
So, technically we want the result of Dt = Δt' - Δt

Homework Equations

Uav = Δx / Δt

The Attempt at a Solution

• 1 h -> 60 min => 2 h -> 120 min => Δt = 165 min
• Uav = 80 km/h = 80/60 km/min
• Uav' = 65 km/h = 65/60 km/min

• Uav'*Δt' = Uav*Δt <=> 65/60 km/min * Δt' = 80/60 km/min * 165 min <=> Δt' = (80 * 165) / 65 min= 203 min

• Dt = Δt' - Δt = (203 - 165) min = 38 min

I also tried turning km to meters, I tried turning 2 h 45 min to 2,75 h, everything. But I still get the same result, every time.

Okay, so, as it's evident it's a simple exercise. The problem is, I've run it 5 times or so, but I get a different result from the book's (no complete solution there, just the end result). The book says that we spent 43 min extra on the road.

Personally speaking, on most occasions (sometimes I approach it with h, and others with min) I get 38 min extra. So, yeah, am I missing something, or does the book have a typo?

PS: It's exercise 2.3 of Hugh D. Young's University Physics, Vol 1

PS2: If anyone has this book, is there any reason why it has the answers only for the odd number exercises?

PS3: If it's of any importance, the book has been translated into Greek from English. You can see from my use of the formulas/equations that I'm still a little wonky on how to accurately write them in their correct form, but University has started for about a month, and the teachers move so fast (in one month, out of the 12 sections, the Physics teacher has already passed the 8th one, so, yeah...) that I'm stuck on my own. Every bit of help would be greatly appreciated!

 

[TomHart]

I tend to look at this things in simple ways. (Simple methods for simple minds.) Can't you just calculate the distance traveled in case 1 and work from there? Edit: For this problem, it looks like it would be easiest to leave the units in km/hr. Then once you get an answer in hours, it may make more sense to convert to minutes.

Giving answers to odd-numbered exercises is fairly common. Professors sometimes want to be able to assign problems that DO NOT have the answers.

Edit2: But now that I worked the problem, I got the same answer: 38 minutes.

Edit3: Foiled again. Billy_joule beat me to the punch. :)

 

[billy_joule]

I agree with your answer. Errors in textbook answers are more common than they should be.

 

[Const@ntine]

I tend to look at this things in simple ways. (Simple methods for simple minds.) Can't you just calculate the distance traveled in case 1 and work from there? Edit: For this problem, it looks like it would be easiest to leave the units in km/hr. Then once you get an answer in hours, it may make more sense to convert to minutes.

Giving answers to odd-numbered exercises is fairly common. Professors sometimes want to be able to assign problems that DO NOT have the answers.

I still get the same result:

Δx = Uav*Δt = 80/60 km/min * 165 min = 220 km

Δt' = Δx/Uav' = (220 km) / (65/60 km/min) = 203 min

Dt = Δt' - Δt = (203 - 165) min = 38 min

As for the answers, I get the why, but dunno, I feel it'd been more helpful to have the answers for all of them. Or at least include a few more examples.

I agree with your answer. Errors in textbook answers are more common than they should be.

Whew, well, that's a relief. Thanks a ton (both for the answer and the link to Wolffram, I had heard about it, but I never got around to using it, since I eventually forgot about it).