Time, Speed, and Distance: The JNVST Arithmetic Topic Everyone Rushes

The Topic That Rewards Slowing Down

Of everything in JNVST arithmetic, time-speed-distance questions are the ones where rushing costs the most marks relative to how little extra time careful reading would take. Going through past papers with our team, the questions themselves are not conceptually harder than a basic distance equals speed times time relationship. What makes them hard is that many of them describe a journey with two different speeds over two different segments, and ask for something that requires treating those segments separately rather than blending them too early.

A Worked Example With Two Different Speeds

Here is a typical setup: "A boy walks to school at 4 km/h and reaches 5 minutes late. If he walks at 5 km/h, he reaches 5 minutes early. What is the distance to school?" A rushed student sometimes tries to average 4 and 5 to get 4.5 km/h and work from there, which does not correspond to anything in the question and leads nowhere useful. The correct approach lets the distance be the unknown, sets up the time taken at each speed as distance divided by speed, and uses the fact that the difference between these two times is 10 minutes, since one is 5 minutes late and the other is 5 minutes early relative to the same target time. Solving distance divided by 4 minus distance divided by 5 equals 10 minutes, expressed in hours as one-sixth, gives a distance of 2 km.

The Trap: Averaging Speeds Instead of Setting Up Time

The specific trap in this section is treating "two speeds" as an invitation to average them, when the actual relationship the question is testing is almost always about the difference or sum of the times taken, not the speeds themselves. Average speed is only ever mathematically valid for equal distances or equal times, and even then it is total distance divided by total time, not a plain average of the two speed values.

Why the Simple Average Feels So Reasonable

Averaging two numbers is one of the most automatic operations in arithmetic, and when a question gives exactly two speeds, the instinct to average them feels like it is using both pieces of information given, which feels thorough. The problem is that this instinct answers a question about speed when the exam is actually asking a question about time.

A Habit That Targets This Exact Mistake

For every time-speed-distance question with more than one speed mentioned, have your child write a small two-row table before doing anything else:

• Row 1: speed, time, distance for the first part of the journey.
• Row 2: speed, time, distance for the second part.

Filling in only what is known and leaving the rest blank makes the actual relationship between the two rows, whether it is equal distance, equal time, or a time difference, visible on paper instead of assumed in the head.