Simple puzzle

A man travels at a speed of 5 kph for half of the distance. What speed shall he be doing for the second half, so that his average speed will be 10 kph?

Tell me, Veeky Forums

Come on guys, I thought you were smart.

That was your first mistake.

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

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

It's not my homework.

Oh, so you're here testing Veeky Forums's intelligence with a high-school level problem?

Just tell me.

>3 replies and still no answer

replies and still no answer
fool.

>Says the guy who can't greentext.

>4 replies and still no answer

>5 replies and still no answer

You have an answer, you dummy. Solve for x.

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

Good job, now go turn it in.

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

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.

Thanks for correcting me, bro.

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])

Well done.

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

WOW

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.

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

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.

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))