Relative Motion Practice Questions
Relative motion questions test whether you can decide when speeds should be added, when they should be subtracted, and how a delayed start changes the remaining gap. This page shows the main patterns with worked examples.
The Rules Every Relative Motion Question Uses
Most questions in the pack are built from the same speed, distance, and time relationships. The key is deciding which speed closes the gap.
↔ Rule 1: Moving towards each other means add speeds
When two people or vehicles travel towards each other, the gap closes at their combined speed.
Example: 5 mph and 3 mph towards each other gives a closing speed of 8 mph.
⏱ Rule 2: Time = gap ÷ closing speed
Once you know the gap and the closing speed, divide to find how long it takes to meet.
Example: A 32 mile gap closing at 8 mph takes 32 ÷ 8 = 4 hours.
🏁 Rule 3: Catch-up questions use the speed difference
If one object is chasing another in the same direction, only the extra speed closes the gap.
Example: 40 mph chasing 25 mph closes the gap at 40 - 25 = 15 mph.
⌛ Rule 4: Delays change the starting gap
If one person starts later, subtract the distance already travelled before using combined speed.
Example: 50 mph for 1 hour removes 50 miles from the original gap.
3 Worked Relative Motion Examples
One straightforward, one multi-step, and one classic mistake to avoid.
1. Two Walkers Moving Towards Each Other
Question: Hugo and Ines start walking towards each other along a path that is 32 miles long. Hugo walks at 5 mph and Ines walks at 3 mph. What is their combined speed, and how far has each walker gone when they meet?
Worked Method
Step 1: They are moving towards each other, so add their speeds: 5 + 3 = 8 mph.
Step 2: Time to meet = 32 ÷ 8 = 4 hours.
Step 3: Hugo travels 5 × 4 = 20 miles. Ines travels 3 × 4 = 12 miles.
Tip: Check the two distances add to the original gap: 20 + 12 = 32 miles.
2. One Traveller Starts Later
Question: Jenny and Sunil are 210 miles apart. Jenny starts travelling towards Sunil at 50 mph. One hour later, Sunil starts travelling towards Jenny at 30 mph. What distance remains when Sunil starts, and how far does Sunil travel before they meet?
Worked Method
Step 1: Jenny travels for 1 hour before Sunil starts, so she covers 50 × 1 = 50 miles.
Step 2: Remaining gap = 210 - 50 = 160 miles.
Step 3: Once both are moving, their combined speed is 50 + 30 = 80 mph.
Step 4: Time after Sunil starts = 160 ÷ 80 = 2 hours, so Sunil travels 30 × 2 = 60 miles.
Tip: Do the delay first. The original gap is no longer the gap once both people are moving.
3. Catch-Up Speed Is Not a Sum
Question: A car is 60 miles ahead of a motorcycle on a highway. The car travels at 25 mph and the motorcycle chases it at 40 mph. By how much does one speed exceed the other, and what distance does the motorcycle cover to catch up?
Worked Method
Step 1: Both are travelling in the same direction, so use the speed difference: 40 - 25 = 15 mph.
Step 2: Time to catch up = 60 ÷ 15 = 4 hours.
Step 3: Motorcycle distance = 40 × 4 = 160 miles.
Tip: Add speeds only when the objects move towards each other. For a chase, subtract the slower speed from the faster speed.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Relative Motion pack contains 90 questions across 3 printable test sets, with 180 sub-questions covering combined speed, relative speed, delayed starts, catch-up problems, distance, time, and speed.
Checkout and downloads are securely handled on Etsy.com