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 h
e 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