Calculus derivative question

the radius of a circular juice blot on a piece of paper towel t seconds after it was first seen is modelled by r(t) = (1+2t)/(1+t) where r is measured in centimeters. calculate
i) the time at which the radius of the blot was 1.5 cm (answer should be 1s)
ii) the rate of increase of the are of the blot when the radius was 1.5cm (answer should be 0.25 cm/s)

i)

(1+2t) / (1+t) = 1.5
1 + 2t = 1.5 (1 + t)
1 + 2t = 1.5 + 1.5t
0.5t = 0.5
t = 1

ii)

dr/dt = ((2(1+t) − 1(1+2t)) / (1+t)²
dr/dt = 1 / (1 + t)²

When r = 1.5 cm, t = 1s and
dr/dt = 1 / (1+1)² = 0.25 cm/s

NOTE: This is the rate of increase of the radius, not the rate of increase of the area (which is asked for in question)
To find rate of increase of area, use related rates:

A = πr²

Now differentiate both sides with respect to t:
dA/dt = 2πr dr/dt
dA/dt = 2π (1.5 cm) (0.25 cm/sec) = 0.75 cm²/sec

So, I guess you really were looking for rate of increase in radius (NOT area), especially since the solution you give has units cm/sec instead of cm²/sec (which we would expect with change in area)

i) 1.5 = (1 + 2t)/(1 + t)
1.5(1 + t) = 1 + 2t
1.5 + 1.5t = 1 + 2t
0.5 = 0.5t
t = 1

ii) d/dt(r(t)) =
(2(1 + t) - 1(1 + 2t))/(1 + t)^2 =
(2 + 2t - 1 - 2t)/(1 + t)^2 =
1/(1 + t)^2
Rate of increase when radius was 1.5 cm =
d/dt(r(1)) = 1/(1 + 1)^2 = 1/2^2 = 0.25cm/s