Question

Solve the Following Word Problem.
Places A and B are 30 km apart and they are on a st raight 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

Let the speed of Hamid be x km/h and that of Joseph be y km/h.
When both travel in same direction so, the distance covered by them together will be 30 km. 
We know \[\text{ Speed }= \frac{\text{ Distance }}{\text{ Time }}\]
They meet each other after 20 min = \[\frac{20}{60} = \frac{1}{3}\]  hours ....(1 hour = 60 min)
\[\frac{x}{3} + \frac{y}{3} = 30\]
\[ \Rightarrow x + y = 90 . . . . . \left( I \right)\]
When Joseph started from point B but moved in the opposite direction. 
Distance travelled by Hamid -  Distance travelled by Joseph = 30
\[\Rightarrow 3x - 3y = 30\]
\[ \Rightarrow x - y = 10 . . . . . \left( II \right)\]
Adding (I) and (II) we get
\[2x = 100\]
\[ \Rightarrow x = 50\]
Putting the value of x in (II) we get
\[50 - y = 10\]
\[ \Rightarrow y = 40\]
Thus, speed of Hamid is 50 km/h and that of Joseph is 40 km/h.