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

Answer:

The jeep will catch up the bike at a distance of 1km

SOLUTION :

Speed of motor bike=72 km/hr=72x5/18 =20 m/s

Speed of Jeep=90x5/18=25m/s

Let us assume that Jeep catches the bike at a distance of  X m from the turning.

Time taken to civer  distance X m =Distance/time

=x/20 sec

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

Time taken to cover X m will be =x/20 - 10

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

These two must be equal. Hence

x/20-10=x/25

x-200/20=x/25

x-200/4=x/5

5x-1000=4x

x=1000m=1km

Answer 2

At 1 km far from the turning the jeep catch up with the bike.

Explanation:

Step 1:

Motor bike speed = 72 km/hr

Converting Kilometer per hour to meter per second  

                    $u=72 \times \frac{5}{18}=20 \frac{m}{s}$

Jeep speed = 90 km/hr

Converting Kilometer per hour to meter per second  

                     $u=90 \times \frac{5}{18}=25 \frac{m}{s}$

Step 2:

Let's suppose Jeep is catching the bike at a distance of X m from the turn.

Time taken to reach X in,    $m=\frac{\text { distance }}{\text { time }}$

                                                $=\frac{x}{20} m$

As jeep starts 10 seconds later, so 10 sec less time is needed to cover the same distance,

Time will be taken to cover X m $=\frac{x}{20}-10$

But it comes to $\frac{x}{25}$ seconds from the speed of the jeep

Step 3:

The two must be comparable.      

Hence,         $\frac{x}{20}-10=\frac{x}{25}$

                        $\frac{x-200}{20}=\frac{x}{25}$

                     $x-200=\frac{20 \times x}{25}$          

               $25(x-200)=20 \times x$

               $25 x-200 \times 25=20 x$

                      $25 x-5000=20 x$

                        $25 x-20 x=5000$

                                    $5 x=5000$          

                                      $x=\frac{5000}{5}$

                                      $x=1000 \mathrm{m}=1 \mathrm{km}$

Thus, the jeep will catch the bike at a distance of 1km.