Two routes X and Y between the same places are respectively 30 km and 20 km long. A person travelling at a uniform speed of 30km/h, goes along route X and realises mid‐way that it has been closed. He takes a connecting route which brings him to the midpoint of route Y and continuing on Y he reaches the destination in one hour. How much time did he spend on the connecting route?

Concept:

The velocity of any object which is travelling is given as: \(velocity=\frac{distance}{time}\)

Explanation:

• Route X is : 30 km long
• Route Y is : 20 km long
• Total journey is of 60 minutes.
• Person chooses route X and travels half way which is : 15km

Now, time taken to travel 15 km with the speed of 30 km/h is : \(t=\frac{15km}{30km/h}=\frac12h\)

Now, after reaching the midpoint of route Y, the person travels distance 10 km with speed of 30 km/h. So, the time taken is: \(t=\frac{10km}{30km/h}=\frac13h\)

So, from the midpoint of the route Y, the time taken is 20 min.

Summarising the journey: Route X takes 30 min, route Y takes 20min. So, the remaining time 10 minutes is spend on the connecting route.