let

f(n) = the number of minutes read per day in the n-th week

f(0) = 20 min the first week

f(1) = f(0) + 0.50*f(0) = 1.50*f(0)

f(2) = f(1) + 0,50*f(1) = 1.50*f(1) = ((1.50)^2)*f(0)

....

f(n) = ((1.50)^n)*f(0)

we can prove this formula by using Mathematical Induction:

the statement holds for n = 0

lets assume that the statement holds for n = k that is f(k) = ((1.50)^k)*f(0)

for n = k+1 we have

f(k + 1) = f(k) + 0.50*f(k) = 1.50*f(k) = 1.50 * ((1.50)^k)*f(0) = ((1.50)^(k+1))*f(0)

thus the statement holds for n = k+1 by mathematical induction, the statement f(n) holds for all natural n.

Now we have to find n so that f(n) = 60, that is

((1.50)^(n))*f(0) = 60

(1.50^n)*20 = 60 divide both sides by 20

1.50^n = 3

n ln 1.5 = ln 3

n = ln 3 / ln 1.5

n = 2.7 rounded to n = 3

since f(0) is the first week n=3 is the forth week

f(3) = ((1.5)^3)*f(0) = 67.5

in the forth week they will read 67.5 minutes.