Who Arrives First Game

About Prediction

Prediction puts two travellers on the screen, for example a cyclist and a runner, or a car and a train. Each card shows how far the traveller still has to go and how fast it moves. They head for the same finish line, and your task is to decide who will arrive first.

The question is a mental version of the relationship time equals distance divided by speed, and the trick is in the numbers. A traveller who is far away but fast may beat one who is close but slow, and that is not always obvious. On the early levels the arrival times differ by a factor of almost two. By the last levels they are only about ten percent apart, and from level 5 the fast travellers show their speed in kilometres per hour while the slow ones stay in metres per second, which makes the task a little more demanding.

How to play

1. Read the two cards. Each gives a distance in metres or kilometres and a speed in m/s or km/h.
2. Estimate the arrival time of each traveller, as distance divided by speed. Rough estimates are enough for the early levels.
3. Tap the traveller you think will arrive first, or press 1 or 2.
4. The result note gives both arrival times in seconds.

Two travellers head for the same finish. Each card shows the distance left and the speed. Decide who arrives first. Watch the units: speeds can be in m/s or km/h.

How scoring works

A right answer scores 100 and a wrong one 0. In endless mode a round counts as passed if the answer is right. The ratio between the two arrival times is at least 1.9 on level 1 and falls to about 1.1 on level 10, so on the top level you really need to calculate. The timer starts at 14 seconds and falls to 10.

The speeds are based on realistic values, with some random variation: a walker 1.4 m/s, a runner about 4 m/s, a scooter about 5 m/s, a cyclist about 6 m/s, a horse about 12 m/s (43 km/h), a car about 22 m/s (80 km/h) and a train about 40 m/s (144 km/h). Arrival times lie between about 6 and 65 seconds.

What it trains

The game trains quantitative reasoning about rates, one of the most useful and the most commonly misjudged kinds of mental arithmetic. It applies to travel planning, to overtaking on the road, to deciding whether you can cross before a car arrives, and to any comparison of speeds.

The unit switch between m/s and km/h also trains conversion: to go from m/s to km/h you multiply by 3.6, and a quick approximation is to multiply by about 3.5.

Tips for a higher score

• Compute the time for each traveller by dividing the distance by the speed, and round both to friendly numbers. 320 m at 3.8 m/s is about 84 seconds, since 320 divided by 4 is 80.
• Convert km/h to m/s by dividing by 3.6, or by dividing by 4 and adding a little. 72 km/h is 20 m/s.
• If the two cards use the same unit, compare the distance-to-speed ratios directly, without converting anything.
• Watch for traps: a large distance does not mean a late arrival, and a high speed does not mean an early one.
• Use the feedback to check your estimate. After a few rounds you learn the speeds of the seven travellers by heart.

The idea behind it

The relationship between distance, speed and time is the most basic equation of kinematics, and people use it all the time with surprisingly little training. Research on how people judge speeds shows a consistent bias: people tend to underestimate the time needed to cover a distance at a moderate speed when the speed is high, and judge relative speeds better when the objects are similar.

Research into road safety shows that people systematically underestimate the speed of approaching vehicles at a distance and overestimate it at close range, a effect that matters at crossings and junctions. Being able to compute rather than guess is the remedy used in driver education.

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