If the relative speeds of bike 1 and 2 is 35 km/hr, that of 2 and 3 is 75 km/hr and that of 1 and 3 is 40 km/hr, then which of the following bikes are moving in the same direction?
1). 1 and 2
2). 2 and 3
3). 1 and 3
4). 1, 2 and 3
Let the individual speeds of bike 1, 2 and 3 be ‘x1’, ‘x2’ and ‘x3’ km/hr respectively
When two bodies are moving towards each other, i.e. moving in opposite direction, their relative speed is the sum of their individual speeds
While, when two bodies are moving in the same direction, their relative speed is the difference of their individual speeds
Now, let,
Relative speed of bike 1 and 2 = ± x1 ± x2 = 35 ----(1)
Relative speed of bike 2 and 3 = ± x2 ± x3 = 75 ----(2)
Subtracting (1) from (2), we get,
⇒ (± x2 ± x3) - (± x1 ± x2) = 75 - 35
⇒ ± x2 ± x3 ? x1 ? x2 = 40
⇒ ± x3 ? x1 = 40
⇒ ± (x3 - x1) = 40 = Relative speed of bike 1 and 3
? Relative speed of bike 1 and 3 is equal to the difference of their individual speeds
∴ Bike 1 and 3 are moving in the same direction