So, who's it gonna be?

Solution 1 :

The size of the rasenshuriken at time $t$ can be be expressed as $s(t) = 100 m^{3} + 20 \frac{ m^{3}}{s} \cdot t$ .

The amount of size that has been absorbed by Madara at time $t$ can be expressed as $a(t) = 25 \frac{ m^{3}}{s} \cdot t$

The point in time when Madara absorbed the complete rasenshuriken will be when $s(t) = a(t)$ . Let's call this point $t_{1}$ . Then

$100 m^{3} + 20 \frac{ m^{3}}{s} \cdot t_{1} = 25 \frac{ m^{3}}{s} \cdot t_{1}$

$100 m^{3} = 5 \frac{ m^{3}}{s} \cdot t_{1}$

$t_{1} = \boxed{20s}$

Hence, Madara will make it in the last moment.

Solution 2 :

Watch the anime or read the manga

Action simulation, go!

Python 2.7:

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rasenshuriken = 100
growth_rate = 20
absorb_rate = 25
seconds = 20
for second in xrange(seconds):
    rasenshuriken += growth_rate
    rasenshuriken -= absorb_rate
    if rasenshuriken <= 0:
        if second >= 10 and second <= 15:
            print "Madara manages to disperse the jutsu in 10-15 seconds."
        break
if rasenshuriken == 0:
    print "The rasenshuriken is dispersed at the last moment!"
elif rasenshuriken > 0:
    print "Naruto is so gonna rasenshuriken him."
else:
    print "Madara overcomes Naruto."

The difference in dispersion is 5 m^3/s so you divide the initial amount by 5 and it takes 20 s to disperse the original 100 m^3. Hence at the last moment if it took less time for formation then there would not be enough Tim to disperse the original amount.

The rate of dispersion is greater than growing by 5 m^3/sec.Thus the Rasenshuriken whose initial size is 100 m^3,will be disperse in the time 100/5=20 sec. by Madara.

In 1st sec. The size is 95 cubic meter in 2nd sec.size is 90 cubic meter 3rd sec. 85 cubic meter Hence. Using AP a=95, d=-5, n th term=0.... if we solve using : nth term=a+(n-1)d... We get n=20.... Hence in the last moment Madra manges to disperse jutsu....

Since the rate of dipersion is greater than the rate of formation, Madara wins obviously. But since the difference in rates are low, he manages it at the last second. Logic