Brain teaser...?

Question

If a car travels from point A to point B at 20mph, and then back from point B to point A (along the same exact route) at 30 mph, what was the car's average speed?

*Note: the answer is not immediately obvious.

I will post the answer to this riddle in 1 hour from post.

First answerer to correctly respond with supporting work gets best answer. Good luck!

The correct answer is indeed 24 mph.

Answer 1

Let the dist between A and B be S miles.
Then time reqd. in up journey = S/20 hr.
Then time reqd. in down journey = S/30 hr.
Total time reqd. = (S/20 + S/30) = 5S/60 = S/12 hr.
Avg. speed = total dist travelled / time taken = 2S/(S/12) = 24 mph.

Answer 2

24 is correct, but I will show the work.

Assume that it is 60 miles from A to B. It will take 3 hours at 20mph. It will take 2 to come back. In all it will take 5 hours to go 120 miles and that is 24mph.

Answer 3

If p(t) is the position function and Vm is the average speed, then we have:

Vm = [p(tf) - p(ti)]/[tf - ti]

Since the car goes back to the starting point, p(tf) = p(ti), so Vm = 0

No, it is not 24 mph. The average speed of the car is, by definition, the average rate of change of it's position function. Since the initial and final position of the car it's the same, there's no change in position in the time interval considered, hence the average speed is 0.
Try to understand the concept of average rate of change like this: you calculate average speed when you only have information about the initial and final position of a vehicle, but you don't know anything about how the movement itself was made (or you're not interested in how it was made). So, if the initial and final position are the same it makes sense to assume that the vehicle hasn't move at all, so it's average speed is zero. It's a classic problem from a basic course on calculus.

Answer 4

24 mph

Lets assume that the distance between point A and point B is 60 miles.
If a car travels at 20mph from point A to point B, then it takes a total of 3 hours to get from A to B. If a car travels at 30mph from point B to point A, then it takes a total of 2 hours to get from B to A.
This adds up to a total of 5 hours to travel 120 miles.
120 miles / 5 hours = 24mph.

Answer 5

to do this you must make an arbitrary value for the distance between A and B....for simplicity a good distance is 60 miles.

t1(time for trip A-B) = 60/20 = 3hr
t2(time for trip B-A) = 60/30 = 2hr
t(total) = 5hr

the total distance driven is 120 miles

therefore the average speed is 120/5 = 24mph

there ya go

Answer 6

24 mph

Answer 7

24 mph

Answer 8

huhm.... very hard question. My brain'd blow up if i try to solve this but any way, here is my attempt.

x = vt

x = 20t
t = x/20

x = 30t
t = x/30

the total time would be
x/30 + x/20 = x/12

since the distance is the same, that means the car travel twice the distance of x. The total distance would be 2x

2x = v(x/12)
v = 24 mile/hr

hope i get it right

Answer 9

25, I'm not sure if i did this right but 20+30=50 divide it by two and you get 25. 25 mph would be the correct answer.

Answer 10

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