Let us learn about a very interesting concept – Relative Speed.

So far, we were only concerned with one object and its speed. But what if there are two or more objects that are moving at the same time. What do we do then?

In such cases, the concept of relative speed comes to our rescue. So, let’s start with this concept now (at full speed).

Suppose there are two cars – car 1 and car 2 moving on a straight road. Their speeds are S1 and S2 respectively.

In this case, if the two cars are moving in the same direction, their relative speed would be S1 – S2. But, if the two cars are moving in opposite directions, their relative speed would be S1 + S2.

Let us look at some applications of this concept.

Modern day Laila and Majnu are deeply in love with each other and are desperate to meet. So they start driving towards each other at the same time. Laila drives her Mercedes chariot at 130 km/hr while Majnu drives his Ferrari chariot at 120 km/hr. If they live 120 km away from each other, can you calculate the amount of time taken till they meet each other?

Explanation:

Time taken = Distance covered / Relative speed

Now, since Laila and Majnu are driving in opposite directions, their relative speed

= 130 + 120 = 250 km/hr

Thus, Time taken = Distance / Relative Speed = 120 km/250 km/hr = 0.48 hrs

Now, find the distance covered by each of them before the meeting happens?

Distance covered by Laila = Laila’s speed * Time taken = 130 * 0.48 = 62.4 kms

Distance covered by Majnu = Total distance – Distance covered by Laila

= 120 km – 62.4 km

= 57.6 kms

Thus, Laila and Majnu will meet at a point 57.6 kms from Majnu’s starting point.

Note: When time taken is constant, distance covered is proportional to speed.

In other words,

D1/D2 = S1/S2 or S1 = S2 * D1/D2

Let us now turn our attention to a closely related concept of Upstream and Downstream.

Note: When traveling downstream (i.e., along with the current), we need to add the speed of the current to the speed of the boat, ship, etc. to get the total speed. When traveling upstream (i.e., traveling against the current), we need to subtract the speed of the current from the speed of the boat, ship, etc. to get the total speed.

Example: A motorboat can sail 135 km downstream on a river in 1.5 hrs. While going upstream, the same boat can cover 180 km in 3 hrs. Calculate the speed of the river and the speed of the boat in still water.

Explanation:

Do note that still water/ standing water means water that is not moving (i.e., speed of the water = 0). In such cases, the speed of the boat, ship, etc. would not be impacted by the water.

Now, in order to solve this question, let us assume that the speed of the boat is ‘x’ and the speed of the river is ‘y’.

Now, let us find the downstream and upstream speed of the boat.

Here, downstream speed = 135/1.5 = 90 km/hr and upstream speed = 180/3 = 60 km/hr

Now, we know that:

Downstream = Boat speed + river speed = x + y = 90

Upstream = Boat speed – river speed = x – y = 60

Adding the two equations, we get:

2x = 150

Hence, x = 75 km/hr

Putting this value in the above equations gives y = 15 km/hr

Hence, the speed of the boat is 75 km/hr and the speed of the river is 15 km/hr.