Rate

Hint 15 mph =22 ft/sec

Rap

Let R = Rate
Let C= Circumference
Let T = Time

R = R + 15
C = 6
T = T - 1/22 ( .454545 seconds)


15 mph = 22 feet per sec. (raprap's hint)

I don't know

Using ft/s 15 mph=22 ft/s

Initial time for one revolution is t sec
Initial velocity V is 6/t ft/s

Final time for one revolution is (t-1/22) sec
Final velocity V' is 6/(t-1/22) ft/s

V'=(V+22) ft/s

So, by substitution

6/t+22=6/(t-1/22)

(6+22t)/t=6/((22t-1)/22)

(22t+6)/t=132/(22t-1)

(22t+6)(22t-1)=132t

484t^2+110t-6=132t

484t^2-22t-6=0

Solving quadratic--2 real solutions

t=136/999 & t=-1/11

negative time make no sense so

t=136/999 sec

V=6*999/136 ft/s =44.07 ft/s

t'=(136/999-1/22)

and

V'=6/(136/999-1/22)=66.16 ft/s

Check

66.16-44.07=22.9 ft/s Close enough for round off error

Initial velocity 44 ft/s= 30 mph
Final Velocity 66 ft/s= 45 mph

Rap