Suppose that a cyclist began a 374 mi ride across a state at the western edge of the state, at the same time that a car traveli
ng toward it leaves the eastern end of the state. If the bicycle and car met after 5.5 hr and the car traveled 33.433.4 mph faster than the bicycle, find the average rate of each.
This is the concept of relative speed; We are required to calculate the speed of the car and the bicycle. Distance between the car and Bicycle=374 miles Time they met=5.5 hr Speed traveled by bicycle=x Speed traveled by car=x+33.4334 Relative speed=x+(x+33.4334)=(2x+33.4334) mph Distance=speed*time 374=(2x+33.4334)*5.5 374=11x+183.8837 collecting like term we get: 374-183.8837=11x 11x=190.1163 thus; x=(190.1163)/(11) x=17.2833 mph thus the speed of the bicycle was x=17.2833 mph The speed of the car was (x+33.4334)=(17.2833+33.4334)=50.7167 mph
