Speed P6

Jack cycles to his friend's house and then returns home by the same route. He always cycles at 4 km/h when going uphill, 12 km/h when going downhill and 6 km/h when on level ground. If his total cycling time is 2h 20mins, what is the distance he cycles in km?


D1 - uphill, D2 - downhill, D3 - level ground
Time from Home to Friend's house --> D1/4 + D2/12 + D3/6


D3 - level ground, D2 - uphill, D1 - downhill
Time from Friend's house to Home --> D3/6 + D2/4 + D1/12


Total time --> D1 (1/4 + 1/12) + D2 (1/12 + 1/4) + D3 (1/6 + 1/6)
                 = 1/3 D1 + 1/3 D2 + 1/3 D3
                 = 1/3 D

1/3 D --> 2 20/60 = 7/3

D --> 3 x 7/3 = 7 km

7 x 2 = 14 km


The distance he cycles is 14 km.