Question

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike ?

Answer 1

72 km/h =72000/3600 m/s = 20 m/s

90 km/h =90000/3600 m/s = 25 m/s  

Suppose the jeep catches the bike at a distance of x m from the turning. 

Time taken by the bike in covering x m = x/20 s.  

Since the jeep starts 10 s later, so it takes 10 s less time to cover the equal distance. 

So time taken by the jeep in covering x m = (x/20)-10 s. 

But from the jeep's speed it comes to be x/25 s. 

These two times must be equal. 

Equating both times we get, 

(x/20)-10 = x/25, → (x-200)/20=x/25 → (x-200)/4=x/5  → 5x-1000=4x → x=1000 m = 1.0 km.

Answer 2

The solution is given below