Problem Solution
Given:
- Speed of each cab = 74 km/h
- Time gap between two cabs = 28 minutes
- Man meets cabs at interval = 10 minutes
- Direction: Opposite
Step 1: Convert time into hours
28 minutes = 28/60 = 7/15 hours
10 minutes = 10/60 = 1/6 hours
Step 2: Head start distance of first cab
Distance = Speed × Time
= 74 × (7/15)
= 518/15 km
Step 3: Relative speed
Since opposite directions:
Relative speed = 74 + x
Step 4: Apply condition
Distance / Relative speed = Time difference
(518/15) ÷ (74 + x) = 1/6
Step 5: Solve equation
(518/15) × 6 = 74 + x
3108/15 = 74 + x
207.2 = 74 + x
x = 133.2
Final Answer Speed of the man = 133.2 km/h
Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
