Answer to Question #120945 in Classical Mechanics for Vidurjah Perananthan

Question

When driving between two locations, the first half of the route is speed limited to 50 km / h and the second half is limited to 70 km / h. Olle puts the cruise control in his car at 60 km / h and keeps this speed throughout the journey. He believes this will mean that it will take just as long to drive between the resorts, as when he is law-abiding and follows the speed limits. To his surprise, he finds that it differs 2.0 minutes in time.
How far is it between the resorts?

Answer 1

$$t=\frac{D}{V}$$

$$t+\Delta t=\frac{D}{2v_1}+\frac{D}{2v_2}$$

$$\Delta t=\frac{D}{2v_1}+\frac{D}{2v_2}-\frac{D}{V}$$

$$\frac{2}{60}=\frac{D}{2(50)}+\frac{D}{2(70)}-\frac{D}{60}$$

$$D=70\ km$$