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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?

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?

Grade:upto college level

3 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
Sol. VP = 90 km/h = 25 m/s. VC = 72 km/h = 20 m/s. In 10 sec culprit reaches at point B from A. Distance converted by culprit S = vt = 20 × 10 = 200 m. At time t = 10 sec the police jeep is 200 m behind the culprit Time = s/v = 200 / 5 = 40 s. (Relative velocity is considered). In 40 s the police jeep will move from A to a distance S, where S = vt = 25 × 40 = 1000 m = 1.0 km away. ∴ The jeep will catch up with the bike, 1 km far from the turning.
Pratham
13 Points
4 years ago
Culprits speed 20 m/s , police's jeep speed 25 m/s 
Now dist b/w them would be equal to velocity of the culprits bike * time he took to drive the bike =V*T=20*10=200
Now let dist b/w the culprit and the final mmeting position be x so time taken by culprit = time taken by police to arrive at final position =t1=t2= 200+x/25=x/20= x= 800m total dist 800+ initial gap 200.= 1000m =1 k m plz appreciate it
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
 
VP = 90 km/h = 25 m/s.
VC = 72 km/h = 20 m/s.
In 10 sec culprit reaches at point B from A.
Distance converted by culprit(B → A), S = vt = 20 × 10 = 200 m.
At time t = 10 sec the police jeep is 200 m behind the culprit
Relative speed of jeep w.r.t culprit = 25 – 20 = 5 m/s
Time in which the gap is covered by the police = s/v = 200 / 5 = 40 s. 
In 40 s the police jeep will move from A to a distance S, where
S = vt = 25 × 40 = 1000 m = 1.0 km away.
∴ The jeep will catch up with the bike 1 km far from the turning.
 
Thanks and regards,
Kushagra

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