Speed P6

A driver and a motorcyclist both started at the same time to travel to Town B, 540 km from Town A. The car was travelling at an average speed 50 km/h faster than the motorcycle for the first 1.5 h. After that, the motorcyclist doubled his speed to catch up with the car. However, he arrived at Town B slightly more than 6 minutes later than the car. If the motocyclist were to arrive at the same time as the driver, at what speed should he increase to instead?

SM1 SM2  SC      TC       TM2     Remarks
---------------------------------------------------------------------------------
50     100   100                             Not possible as SM2 = SC
60     120   110  4 10/11   3.75      3.75 + 1.5 - 4 10/11 = 0.34 h > 20 min
70     140   120      4.5      3 3/70   3 3/70 + 1.5 - 4.5 = 3/70 h > 6 min

70 x 1.5 = 105 km
540 - 105 = 435 km

540 / 120 = 4.5 h
4.5 - 1.5 = 3 h

435/3 = 145 km/h

He should increase the speed to 145 km/h.