Streetmath

Let C (as in 'car') and B (as in 'bicycle') be two vehicles moving along a road. Let C be behind B, but driving at a higher speed than B, i.e. C will overtake B (on the opposite lane keeping a safety distance of at least 1,50 m). Questions:

1. Given the speed difference between C and B and the total speed of B, how long does it take for C to overtake B?
2. And what distance do both vehicles travel while the overtake takes place?

Assume C and B are points and the road is a straight line. Given quantities:

• $v_C$: speed of the car
• $v_B$: speed of the bicycle
• $w$: relative window size

For example, the driver travels at $v_C$ = 30 km/h, the cyclist at $v_B$ = 20 km/h, and the relative window size is $w$ = 10 m, that is C switches the lane 5 m behind B, passes B, and switches the lane again when C is 5 meters in front of B.