Find the ratio between lorry,van and car.?

Question

A lorry, a van and a car set off at the same time travelling at a constant speed of 60 km/h,80 km/h and 120 km/h. The lorry and the van were travelling from Town G to Town H while the car was travelling from Town H to Town G. The car passed the lorry 2 minutes after passing the van.

a. Find the ratio of the distances travelled by the lorry to the van to the car at the moment when the car passed the van.

b. find the distance between Town G and H.

Answer 1

Lorry speed  =  60 km/hr  =  1 km/min

Van speed  =  80 km/hr  =  4/3 km/min

Car speed  =  120 km/hr  =  2 km/min

After meeting the van, The car travels for 2 minutes before meeting the lorry.

Closing speed of car and lorry  =  (2 + 1) km/min, therefore distance between van and lorry  =  2min x 3 km  =  6 km.

When the car met the van, therefore, the van was  6km ahead of the lorry.

If they had been travelling for t minutes, distance gained over the lorry by the van  =  4.t / 3  - 1.t  =  t / 3

And this distance  =  6 km

So  t / 3  =  6,  hence   t  =  18 minutes.

In 18 minutes the lorry travels  18 km, the van  24 km, and the car 36 km

So the ratios of the distances travelled  L : V : C  =  18 : 24 : 36,  or  3 : 4 :  6

In 18 minutes, the van travels 24 km  and the car  36 km;  so the distance between G and H  =  (24 + 36) km  =  60 km.