Question

A police jeep is chasing a culprit going on a motor bike. 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

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Distance=1\:km}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a police jeep is chasing a culprit going on a motor bike. 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.

• We have to find how far from the turning will the jeep catch up with the bike?

$\underline \bold{Given : } \\ \implies Speed \: of \: jeep =9 0 \: km/h \\ \\ \implies Speed \: of \: motor\: bike = 72 \: km/h \\ \\ \underline \bold{to \: find : } \\ \implies Distance \: when \: jeep \: catches \: bike = ?$

• According to given question :

$\bold{Speed \: of \: jeep = 90 \times \frac{5}{18} = 25 \: m/s} \\ \\ \bold{Speed \: of \: motor \: bike = 72 \times \frac{5}{18} = 20 \: m/s} \\ \\ \bold{Case \: I} \\ \implies When \: jeep \: start \: after \: 10 \: sec \: \\ \\ \bold{For \: motor \: bike : } \\ \implies Distance = speed \times time \\ \\ \implies Distance = 20 \times 10 \\ \\ \bold{\implies Distance = 200 \: m} \\ \\ \bold{ \therefore When \: jeep \: starts \: motor \: bike \: is \: 200 \: m \: ahead} \\ \\ \bold{Case \: II} \\ \\ \bold{Let \: distance \: travelled \: by \: jeep = x \: m}\\ \bold{ and \: time \: T \: to \: catch \: motor \: bike} \\ \\ \bold{For \: jeep : } \\ \implies Distance = speed \times t ime \\ \\ \implies x = 25 \times T \\ \\ \implies T= \frac{x}{25} - - - - - (1) \\ \\ \bold{For \: bike : }$$\implies Distance =( x - 200) \: m\\ \\ \implies time = T\\ \\ \implies speed = 20 \: m/s \\ \\ \implies x - 200 = 20 \times T \\ \\ \implies T = \frac{x - 200}{20} - - - - - (2) \\ \\ \bold{Comparing \: (1) \: and \: (2) \:,\:we \: get} \\ \implies \frac{x}{25} = \frac{x - 200}{20} \\ \\ \implies 20x = 25x - 5000 \\ \\ \implies 20x - 25x = - 5000 \\ \\ \implies - 5x = - 5000 \\ \\ \implies x = \frac{ \cancel{- 5000}}{ \cancel{ - 5}} \\ \\ \bold{\implies x = 1000 \: m} \\ \\ \bold{\therefore After \: 1 \: km \: jeep \: catches \: the \: bike}$

Answer 2

$\huge\sf{Answer:-}$

According to the given question

• A police jeep is chasing a culprit going on a motor bike.

• The motorbike crosses a turning at a speed of 72 kilometer for a hour.

• The jeep follows it at a speed of 90 kilometer per a hour, crossing the turning ten seconds later than the bike.

• In this given question we have to find how far from the turning will the jeep catch up with the bike.

Hence,

according to the 1st case the jeep started after 10 seconds.

Using Formula:-

D = S × T [ Distance = Speed × Time]

So, The distance is equal to 20 mulitplied with 10 [20 × 10] = 200meter is the distance Hence,200m is the

jeep when the motor bike is starting.

according to the 2nd case y be the speed of jeep to catch the time of the bike.

Jeep

$⟶\sf y = 25 \times \: Time \\⟶\sf Time = 25 \times 7 \\ ⟶\sf Time \: = \frac{y}{25} - - Equation - (1)$

Motor Bike

$⟶\sf y - 200 \\ ⟶\sf 20 \: Meter = Speed \\⟶\sf y - 200 = 20 \times Time \\ ⟶\sf Time = \frac{y - 200}{20} - - Equation - (2)$

Both equation (1) - (2)

$⟶\sf \frac{y}{25} = \frac{y - 200}{20} \\ ⟶\sf 20y = 25y - 500 \\ ⟶\sf - 5y = - 500 \\⟶ y = \frac{ - 500}{5} = 1000meter$

1,000 meter => 1 kilometer

Hence, 1kilometer is the answer.