Time, speed and distance questions, with answers

The questions, with answers

1. 1.What is the core formula, and how do you convert between km/h and m/s?

   Distance = Speed × Time, and the two rearrangements. Units are where marks go: train questions give lengths in metres and speeds in km/h, so convert before anything else. Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h. 90 km/h is 90 × 5/18 = 25 m/s. 20 m/s is 20 × 18/5 = 72 km/h. Memorise 36 km/h = 10 m/s and 72 km/h = 20 m/s as anchors; most question setters pick multiples of 18.

2. 2.How do you find the average speed of a journey?

   Total distance divided by total time — never the average of the speeds. When the two halves of a journey cover the same distance at speeds x and y, the average speed is 2xy / (x + y), which is always less than the arithmetic mean because more time is spent at the slower speed.

   Example: 60 km/h going, 40 km/h returning over the same road. Average = 2 × 60 × 40 / 100 = 48 km/h, not 50. When the times (not the distances) are equal, the plain average does apply — read which one the question fixes.

3. 3.How do relative speed problems work?

   Two objects moving in opposite directions approach each other at the sum of their speeds; in the same direction, the faster gains on the slower at the difference. A train passing another train must cover the sum of both lengths at the relative speed.

   Example: trains of 100 m and 200 m at 72 km/h and 36 km/h. Opposite directions: relative speed 108 km/h = 30 m/s, distance 300 m, time 10 s. Same direction: relative speed 36 km/h = 10 m/s, time 30 s.

4. 4.How long does a train take to cross a pole versus a platform?

   To cross a pole (or a standing person, or a signal), the train covers its own length. To cross a platform or bridge, it covers its own length plus the platform's, because the rear of the train has to clear the far end. Forgetting to add the train's length is the single most common error on this topic.

   Example: a 150 m train at 54 km/h (15 m/s) crosses a pole in 150 / 15 = 10 s, and a 300 m platform in (150 + 300) / 15 = 30 s.

5. 5.How do boats and streams questions work?

   Downstream speed = boat speed + stream speed; upstream speed = boat speed − stream speed. Going the other way, boat speed = (downstream + upstream) / 2 and stream speed = (downstream − upstream) / 2. "Speed in still water" means the boat's own speed.

   Example: 12 km/h downstream and 8 km/h upstream gives a boat speed of 10 km/h and a stream speed of 2 km/h. When a question gives distances and total times for two trips, set d/(b + s) + d/(b − s) = t for each and solve the pair.

6. 6.How do you solve "late by x minutes, early by y minutes" problems?

   For a fixed distance, time is inversely proportional to speed. If walking at speed s₁ makes you late by t₁ and at s₂ makes you early by t₂, the two journeys differ in time by t₁ + t₂, and distance = s₁ × s₂ × (t₁ + t₂) / (s₂ − s₁), with the time in hours.

   Example: at 4 km/h a student is 10 minutes late; at 5 km/h, 5 minutes early. The difference is 15 minutes = 0.25 h. Distance = 4 × 5 × 0.25 / (5 − 4) = 5 km. Check: 5 km takes 75 minutes at 4 km/h and 60 minutes at 5 km/h — 15 minutes apart, as required.

7. 7.When do two runners on a circular track meet?

   On a track of length L, runners at speeds a and b (a > b) starting together meet every L / (a − b) seconds if they run the same way — the faster must gain a full lap — and every L / (a + b) if they run opposite ways, since together they cover one lap between meetings. They are both back at the start together after the LCM of their individual lap times.

   Example: 600 m track, 8 m/s and 5 m/s. Same direction: 600 / 3 = 200 s. Opposite: 600 / 13 ≈ 46.2 s.

8. 8.What are the traps that cost the most marks on this topic?

   Four, in order of frequency. Mixing units — metres with km/h — without converting. Averaging speeds arithmetically when the distances are equal. Dropping the train's length when it crosses a platform, or adding it when it only passes a pole. And reading "same direction" as "add the speeds". Each of these produces one of the wrong options on purpose; question setters build the distractors from exactly these mistakes, so if your answer matches an option after a shortcut, that is not confirmation it's right.

How the diagnostic asks it

One question from the Aptitude bank, exactly as a sitting would show it. The bank has 3 on time, speed and distance and 30 across Aptitude.