Time, Speed and Distance Question 2 - CAT 2024
A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is:
Step-by-Step Explanation
Let the scheduled travel time of the bus be t hours and the total distance of the route be D km.
Analyze Day 1:
Traveling at 60 km/h, the bus arrives 3.5 hours late.
D = 60 × (t + 3.5) --- (Equation 1)
Analyze Day 2:
The bus covers 2/3 of the route in 1/3 of the scheduled time.
Remaining distance = 1 − 2/3 = 1/3 D
Remaining time = 1 − 1/3 = 2/3 t
To arrive exactly on time, the bus covers this remaining section at 40 km/h:
Speed = Remaining Distance / Remaining Time
= (1/3 D)/(2/3 t) = D/(2t) = 40 km/h
D/t = 80 km/h
The regular scheduled speed of the bus (D/t) is exactly 80 km/h, so:
D = 80t
Equate the distance expressions:
80t = 60(t + 3.5)
80t = 60t + 210
20t = 210 ⟹ t = 10.5 hours
Determine Scheduled Arrival Time:
The journey starts at 9:00 am and normally takes 10.5 hours (10 hours and 30 minutes).
Arrival Time = 9:00 am + 10 hours 30 minutes = 7:30 pm
Correct Option: A
💡 FundaMakers Tip:
Focus on the ratio of remaining values on Day 2. Covering 1/3 of the distance in 2/3 of the time implies that the speed on this section is exactly half of the required average scheduled speed. Since this secondary speed is 40 km/h, the scheduled speed must be 40 × 2 = 80 km/h. Comparing the speed ratios (80 : 60 = 4 : 3) means the time ratio is inversely 3 : 4. The extra 1 unit represents 3.5 hours, so the standard scheduled time is 3 × 3.5 = 10.5 hours.