let

x = the rate of ascent

y = the rate of descent

d = the distance she bikes up the mountain = the distance she bikes down the mountain

t1 = 4 h the time she biked up the mountain

t2 = 3 h the time she biked back the same distance

her rate of ascent was 1.5 km/h less than her rate of descent

x = y - 3

the distance she bikes up the mountain = the distance she bikes down the mountain

t1*x = t2*y

4*x = 3*y

by solving the system of equations

x = y - 3

4*x = 3*y

we find

x = 9 km/h

y = 12 km/h

d = 4 * 9 = 36 km

Rieko went 36 km up the mountain and then another 36 kn down therefore she biked 36 + 36 = 72 km in total.