Shortcut Trick
Test the options to satisfy the condition: (Distance ÷ Reduced Speed) − (Distance ÷ Usual Speed) = Time Difference
Given Distance = 960 km and Time Difference = 4 hr. Let Usual Speed = 120 km/hr.
Reduced Speed = 120 − 40 = 80 km/hr.
Check: (960 ÷ 80) − (960 ÷ 120) = 12 − 8 = 4 hr.
The condition is satisfied for 120 km/hr.
∴ The correct answer is 120 km/hr.
Alternate Method
Given:
Total Distance (D) = 960 km
Time Difference (Δt) = 4 hr (early departure adjustment)
Speed Decrease (Δv) = 40 km/hr
Formula Used:
Distance = [v × (v − Δv) ÷ Δv] × Δt, where v is the usual speed.
Calculations:
⇒ 960 = [v × (v − 40) ÷ 40] × 4
⇒ 960 = [v × (v − 40)] ÷ 10
⇒ 9600 = v2 − 40v
⇒ v2 − 40v − 9600 = 0
⇒ v2 − 120v + 80v − 9600 = 0
⇒ v(v − 120) + 80(v − 120) = 0
⇒ (v − 120)(v + 80) = 0
⇒ v = 120 or v = −80
Since speed cannot be negative, v = 120 km/hr.
∴ The correct answer is 120 km/hr.
Additional Information
Distance, Speed, and Time Relation
The fundamental relation is Distance = Speed × Time. When distance is constant, speed and time are inversely proportional (s1 × t1 = s2 × t2).
Time Difference Formula
If a body changes its speed from v1 to v2 and the difference in time taken to cover distance D is Δt, then D = [v1 × v2 ÷ |v1 − v2|] × Δt.
Average Speed
For a journey where two equal distances are covered at speeds 'x' and 'y', the average speed is given by 2xy ÷ (x + y).