How is the time to catch up calculated?

Time = head start distance ÷ (chaser speed − leader speed). The speed difference is the distance closed per unit time, called the closing speed, and the chaser must be faster than the leader or a catch-up never happens.

When should I use this instead of the meeting travel problem?

A catch-up problem has both moving in the same direction, so you divide by the difference of their speeds. A meeting problem has them moving toward each other, so you divide by the sum of their speeds — use the meeting calculator for that.

What if I only know the head-start time, not the distance?

You can derive the head-start distance as leader speed × time gap. The distance to the catch-up point is then the chaser speed × the time to catch up.

Catch-Up Travel Problem Calculator

Find the time to catch up and the distance to the meeting point from the leader speed, chaser speed, and head start distance or time gap.

Last updated: June 27, 2026

Input

From the leader and chaser speeds plus the head start distance (or time gap), find how long it takes to catch up.

Leader speed

per hour

Chaser speed

per hour

How the head start is given

Head start distance

dist

How far ahead the leader is when the chaser starts.

Result

Time to catch up

2hours

Distance to meeting point

160 dist

Distance closed per hour

20 per hour

Head start distance

40 dist

Working

Find the speed difference. 80 minus 60 equals 20, the distance closed each hour.

Divide the head start by the speed difference. 40 divided by 20 equals 2, the time to catch up.

Multiply the chaser speed by the time. 80 times 2 equals 160, the distance to the meeting point.

How it works

The catch-up time equals the head start distance divided by the difference in speeds. Time equals head start divided by chaser speed minus leader speed.
The speed difference is the closing speed, the distance closed per unit of time. The chaser must be faster than the leader to ever catch up.
Enter the head start distance directly, or derive it from a time gap as leader speed times the time gap.
The distance to the meeting point equals the chaser speed times the catch-up time.

Frequently asked questions

How is the time to catch up calculated?: Time = head start distance ÷ (chaser speed − leader speed). The speed difference is the distance closed per unit time, called the closing speed, and the chaser must be faster than the leader or a catch-up never happens.
When should I use this instead of the meeting travel problem?: A catch-up problem has both moving in the same direction, so you divide by the difference of their speeds. A meeting problem has them moving toward each other, so you divide by the sum of their speeds — use the meeting calculator for that.
What if I only know the head-start time, not the distance?: You can derive the head-start distance as leader speed × time gap. The distance to the catch-up point is then the chaser speed × the time to catch up.

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