Peter travels to his uncle's home 30km away from his place.He cycles for two thirds of the journey before the bicycle develops a mechanical problem and he has to push it for the rest of the journey. If his cycling speed is 10km/hr faster than his walking speed and he completes the journey in 3hr 20minutes, determine his cycling speed?

Accepted Solution

Answer:Cycling Speed is 15km/hrStep-by-step explanation:Let the cycling speed of Peter be xkm/hrHis walking speed is (x-10km/hr)Distance cycling is 2/3 x 30 = 20kmDistance walking 1/3 x 30 = 10kmTime taken in cycling = distance/ speedTime = 20/xThis gives 20/x km/hrTime walking is 10 / (x-10)= 10/x-10) hrsTotal time = (20/x + 10/x+10)Therefore 10/x+10/x-10 = 10/360(x-10)+30(x)=10x(x-10)10x² - 190x+600=0x²-19+60=0x=19±√361-240         2x=15 0r x =4His cycling speed is 4