Shortcut Trick
When a train passes two objects moving in the same direction, the length of the train remains constant.
Speed of Train = (v2 × t2 − v1 × t1) ÷ (t2 − t1)
Speed of Train = (15 × 11 − 10 × 10) ÷ (11 − 10)
Speed of Train = (165 − 100) ÷ 1
Speed of Train = 65 km/hr
∴ The correct answer is 65 km/hr.
Alternate Method
Given:
Speed of 1st bicycle = 10 km/hr
Speed of 2nd bicycle = 15 km/hr
Time to pass 1st bicycle (t1) = 10 sec
Time to pass 2nd bicycle (t2) = 11 sec
Train (v km/h)
B1
10 km/h
t&sub1; = 10 sec
Train (v km/h)
B2
15 km/h
t&sub2; = 11 sec
Length = Relative Speed × Time (Constant)
Formula Used:
Distance = Relative Speed × Time
Relative speed (same direction) = Speed of Train − Speed of Object
Calculations:
⇒ Let the speed of the train be v km/hr.
⇒ Length of the train passing B1 = (v − 10) × (5 ÷ 18) × 10
⇒ Length of the train passing B2 = (v − 15) × (5 ÷ 18) × 11
⇒ Since the length of the train is constant in both cases, we can equate them:
⇒ (v − 10) × (5 ÷ 18) × 10 = (v − 15) × (5 ÷ 18) × 11
⇒ (v − 10) × 10 = (v − 15) × 11
⇒ 10v − 100 = 11v − 165
⇒ 11v − 10v = 165 − 100
⇒ v = 65 km/hr
∴ The correct answer is 65 km/hr.
Additional Information
Relative Speed (Same Direction)
When two bodies are moving in the same direction, their relative speed is the difference of their individual speeds: Relative Speed = |V1 − V2|.
Relative Speed (Opposite Direction)
When two bodies are moving in opposite directions towards or away from each other, their relative speed is the sum of their individual speeds: Relative Speed = V1 + V2.
Unit Conversion Rule
To convert speed from km/hr to m/s, multiply the value by (5 ÷ 18). Conversely, to convert from m/s to km/hr, multiply by (18 ÷ 5).