Time, Speed and Distance Question 1 - CAT 2025
Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is:
Step-by-Step Explanation
Analyze the Time AP:
Total travel time = 3 hours = 180 minutes. The times taken for the four parts form an Arithmetic Progression (AP) starting with t₁ = 30 minutes.
Let the common difference for time be d.
Total Time = 30 + (30 + d) + (30 + 2d) + (30 + 3d) = 180
120 + 6d = 180 ⟹ 6d = 60 ⟹ d = 10 minutes
The times taken for the four parts are: t₁ = 30 min, t₂ = 40 min, t₃ = 50 min, and t₄ = 60 min.
Analyze the Speed AP:
The total distance traveled is 224 km = 224,000 meters. The speeds form an AP starting with s₁ = 960 m/min.
Let the common difference for speed be x m/min.
s₁ = 960
s₂ = 960 + x
s₃ = 960 + 2x
s₄ = 960 + 3x
Set up the Total Distance Equation:
Total Distance = (s₁t₁) + (s₂t₂) + (s₃t₃) + (s₄t₄) = 224,000
(960 × 30) + (960 + x)40 + (960 + 2x)50 + (960 + 3x)60 = 224,000
960(30 + 40 + 50 + 60) + 40x + 100x + 180x = 224,000
960(180) + 320x = 224,000
172,800 + 320x = 224,000
320x = 51,200 ⟹ x = 51,200/320 = 160 m/min
Calculate the Distance for the Fourth Part:
Speed for Part 4 (s₄) = 960 + 3(160) = 960 + 480 = 1440 m/min
Distance for Part 4 = s₄ × t₄ = 1440 m/min × 60 min = 86,400 meters
Correct Option: D
💡 FundaMakers Tip:
When handling mixed AP workflows, keep units consistent. Converting kilometers to meters at the very beginning aligns the equation with the given speed unit (meters per minute). Factor out the common base value (960) to minimize arithmetic multiplication clutter.