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?

Cycling Speed is 15km/hr

Step-by-step explanation:

Let the cycling speed of Peter be xkm/hr

His walking speed is (x-10km/hr)

Distance cycling is 2/3 x 30 = 20km

Distance walking 1/3 x 30 = 10km

Time taken in cycling = distance / speed

Time = 20/x

This gives 20/x km/hr

Time walking is 10 / (x-10)

= 10/x-10) hrs

Total time = (20/x + 10/x+10)

Therefore 10/x+10/x-10 = 10/3

60 (x-10) + 30 (x) = 10x (x-10)

10x² - 190x+600=0

x²-19+60=0

x=19±√361-240

2

x=15 0r x = 4

His cycling speed is 4