Two bodies moving from point A

[fawk3s]

Homework Statement

One body starts moving from point A so that in first min it goes 3 m/min, and in every next minute it goes 6 m more that in the minute before. Another body starts moving from point A 5 minutes later, going 54 m/min in the first minute and in every other minute 3 m more that in the minute before. After how many minutes have the bodies traveled the same distance? (Time starting after the second body starts its movement.)

Homework Equations

s=v₀t+at²/2

where s - distance
v₀ - initial velocity
a - acceleration
t - time

The Attempt at a Solution

I already know how you can solve this using arithmetic progression. But what I can't understand is why doesn't the distance equation from physics apply in this. It ought to!

So what I did was this:

s1=s2

s1=3(t+5)+6(t+5)²/2
s2=54t+3t²/2

3(t+5)+6(t+5)²/2=54t+3t²/2

t=1,5t²-21t+75,

which doesn't work out. What am I doing wrong here?

Thanks in advance,
fawk3s

 

[fawk3s]

Ok, I think I figured it out now. I guess you can't take those "goes 6 m more in the next minute" as an acceleration.
This thinking made my head hurt :(