Question

Places $A$ and $B$ are $30km$ apart and thery are on a straight road. Hamid travels from $A$ to $B$ on bike. At the same time Joseph starts from $B$ on bike, travels towards $A$. They meet each other after $20$ minutes. If Joseph would have started from $B$ at the same time but in the opposite direction (instead of towards $A$) Hamid would have caught him after $3$ hours. Find the speed of Hamid and Joseph.

Answer 1

R.E.F image

Let speed of Hamid = $H$ km/hr

Let speed of Joseph = $J$ km/hr

Then when they travel in opposite direction

$x=H\times \frac{1}{3}$

$30-x=J\times \frac{1}{3}$

$\Rightarrow 30-H/3=J/3$

$\Rightarrow J=90-H...\left(i\right)$

When same direction & meet at C

$D=J\times 3$

$30+D=3H$

$30+3J=3H...\left(ii\right)$

On solving eq${}^n$ (i) & (ii) we get

H = 50 km/hr & J = 40 km/hr