
Shortcut Trick
Apply Alligation on Speeds to find the Time Ratio: Foot (5) vs Cycle (12) with average (45/7).
Time ratio = (12 − 45/7) : (45/7 − 5) ⇒ (84 − 45)/7 : (45 − 35)/7 = 39 : 10.
Total time units = 39 + 10 = 49 units, which corresponds to 7 hours.
Time on foot = (39 ÷ 49) × 7 = 39/7 hours.
Distance on foot = Speed × Time = 5 × (39/7) = 195/7 ≈ 27.86 km.
∴ The correct answer is approx.28km.

Alternate Method
Given:
Total Distance = 45 km
Total Time = 7 hours
Speed on Foot (v1) = 5 km/hr
Speed on Cycle (v2) = 12 km/hr

Calculations:
Let the time spent traveling on foot be 't' hours.
Then, the time spent traveling on cycle = (7 − t) hours.
⇒ Total Distance = (Speedfoot × Timefoot) + (Speedcycle × Timecycle)
⇒ 45 = 5 × t + 12 × (7 − t)
⇒ 45 = 5t + 84 − 12t
⇒ 45 − 84 = −7t
⇒ −39 = −7t
⇒ t = 39/7 hours
⇒ Distance covered on foot = Speedfoot × t
⇒ Distance = 5 × (39/7) = 195/7
⇒ Distance ≈ 27.857 km
∴ The correct answer is approx.28km.

Additional Information
Average Speed
Average speed is defined as the total distance traveled divided by the total time taken: Average Speed = Total Distance ÷ Total Time.
Alligation Method for Time and Distance
When alligation is applied to speeds, the resulting ratio is the ratio of time taken for each part of the journey.
Relationship between Speed and Time
For a constant distance, speed is inversely proportional to time (S ∝ 1/T). For constant time, distance is directly proportional to speed (D ∝ S).