A bicyclist started on his trip from city A to city B. In 1 hour and 36 minutes, a biker also left A and headed towards B, and he arrived there at the same time as the bicyclist. Find the speed of the bicyclist if it is less than the speed of the biker by 32 km/hour, and the distance between the two cities is 52 km.

Speed of first bicyclist=x

Speed of biker = x+32

Convert 1 hour and 36 min to hours.

1+36/60 = 1.6 hours

Bicyclist time is 1.6 hours longer than biker.

Equation is:

52/x - 1.6 = 52 / (x+32)

Solve for x.

52 (x+32) - 1.6 (x+32) = 52x

5x+1664-1.6x²-51.2x=52x

Simplify

1.6x²+51.2x-1664=0

Using quadratic formula.

We get

x=20 km per hour which is the speed of the Bicyclist.

Now speed of biker = 20+32=52 km/hr

Answer: Speed of Bicyclist = 20 km/hr