A men covered a certain distance of one side by cycle and other side by scooter in 2 hours 20 minutes. If he had covered the total distance by cycle then time consumed was 3 hours 30 minutes. In what time he can cover the distance by scooter ?

Let the total distance = $$2x$$ km , then distance of one side = x km

Let speed of cycle = $$c$$ km/hr and speed of scooter = $$s$$ km/hr

Acc. to ques, => $$\frac{2x}{c} = 3 \frac{1}{2}$$

=> $$\frac{x}{c} = \frac{7}{4}$$

Also, $$\frac{x}{c} + \frac{x}{s} = 2 \frac{1}{3}$$

=> $$\frac{7}{4} + \frac{x}{s} = \frac{7}{3}$$

=> $$\frac{x}{s} = \frac{7}{3} - \frac{7}{4} = \frac{7}{12}$$

Since, total distance = $$2x$$, multiplying both sides by 2, we get :

=> $$\frac{2x}{s} = \frac{7}{6}$$

Thus, total time taken to cover the distance by scooter = $$\frac{7}{6} \times 60 = 70$$ minutes

= 1 hr 10 minutes