Simple puzzle

>>8492008
Come on guys, I thought you were smart.

>>8492016
That was your first mistake.

>>8492008
>>8492016
>common i thought you were smart!
We're not going to do your homework for you.

5 * (.5) + x * (.5) = 10(1)

>>8492022
It's not my homework.

>>8492027
Oh, so you're here testing /sci/'s intelligence with a high-school level problem?

>>8492029
Just tell me.

>3 replies and still no answer

>>8492031
>>3 replies and still no answer
fool.

>>8492039
>Says the guy who can't greentext.

>>8492039
>4 replies and still no answer

>>8492044
>5 replies and still no answer

>>8492047
>>8492045
>>8492031
You have an answer, you dummy. Solve for x.

>>8492058
15 kph is clearly a wrong result (as is the equation).

>>8492062
Good job, now go turn it in.

>>8492022
That is wrong, there you are assuming "equal times" instead of "equal space".

>>8492008
The answer is infinity.
v_total=2(v_1)*(v_2)/(v_1+v_2)
therefore
v_2=(v_total)*(v_1)/[(v_total)-2(v_1)]
so, when v_total=2*v_1 we have infinity.

>>8492069
Thanks for correcting me, bro.

>>8492067
What do you mean? You averaged by the distance, I've never seen anyone do that, and the question is obviously talking about the standard average (i.e. by time v(avg) = [v1t1 +v2t2]/[t1 + t2])

>>8492069
Well done.

File: yHkVqVe.png (453KB, 525x632px) Image search: [Google]

453KB, 525x632px

>go 5km in the first hour
>go 15km in the second hour
>I have gone 20km in 2 hours

WOW

>>8492029
This is a well-known paradox so clearly not just a homework problem.
It's intuitively pretty easy to see that his average speed (averaged over the entire distance) is already 10kph precisely at the moment when he has traveled half the distance at 5kph, any further traveling can only bring that down.

>>8492079
Oops, nvm. Reading comprehension less than or equal to 0.

>>8492008
It's easy:
Assume the distance is x km.
therefore , for the first x/2 km, v̄ = 5[km/h] / 0,5*x [km]

now we know v̄ of the full distance is 10[km/h].
and the formula for v̄ is Δs / Δt.
and Δs = x [km].
and Δt = (0,5*x[km]) / 5[km/h] + (0,5*x[km]) / y[km/h]

therefore x[km] / ((0,5*x[km])/5[km/h] + (0,5*x[km])/y[km/h] ) = 10

Do the solving yourself.

>>8492308
Here's the solution for a function f(x) that returns the required speed for a distance x:

f(x) = (5*x^2)/(1-10*((0,5*x^2 )/5))