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Solve the following :

Question:

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of $72 \mathrm{~km} / \mathrm{h}$. The jeep follows it at a speed of $90 \mathrm{~km} / \mathrm{h}$, 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?

Solution:

$V_{\text {bike }}=72^{\times \frac{5}{18}}=20 \mathrm{~m} / \mathrm{s}$

$\mathrm{V}_{\text {police }}=90^{\times \frac{\mathrm{N}}{18}}=25 \mathrm{~m} / \mathrm{s}$

Distance travelled by culprit in $10 \mathrm{sec}=$ speed $\times$ time

$=20 \times 10$

$=200 \mathrm{~m}$

Time to catch culprit by police=Relative distance/Relative speed

$=\frac{200}{(25-20)}$

$\mathrm{T}=40 \mathrm{sec}$

So, police travels distance of $=25 \times 40$

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

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