let speed of otto =x, and speed of han = h

Let's breakdown this question into three different segments, namely t0,t1, and t2. now, lets see what's happening in the each segment.

As can be seen in the above pic, the initial distance between otto and han is 60 km. After time t=t0, they start moving towards other at their respective rate of x and h respectively.

now suppose at time t=t1, they meet each other at point z.

Therefore total distance traveled by otto and han, when they met at point z is equal to 60.

thus, t1 = \(\frac{60}{(x+h)}\) ----------------------------------------1)

Now, from point z, they again start moving in their respective directions at their constant rates, until the distance between them becomes 60.

so, at time t=t2, distance between otto and han becomes 60.

thus, t2 = \(\frac{60}{(x+h)}\) -------------------------------------------2)

also, as per the question t1+t2=(3/2) hours

now, put the value of t1 and t2 from 1 and 2, we have

\(\frac{60}{(x+h)}\) + \(\frac{60}{(x+h)}\) = 3/2

x+h =80

or h=80-x