How to Find When Two People Meet

Two people set some distance apart walk towards each other. To find how long it takes them to meet, divide the distance between them by the sum of their speeds.

$d$ is the distance between them, $a$ and $b$ are their speeds and $t$ is the time until they meet. The distance each one covers, $at$ and $bt$, is shown as well.

Why the speeds are added

Walking towards each other, the gap shrinks in every minute by what A covers and by what B covers together, so it closes by $a + b$ a minute. The gap to close is $d$, which makes the time $d$ divided by $a + b$.

Example

Two people 1800 m apart walk towards each other at 70 m and 50 m a minute. The gap closes by $70 + 50 = 120$ m a minute, so $t = 1800 \div 120 = 15$ minutes. In that time A covers $70 \times 15 = 1050$ m and B covers $50 \times 15 = 750$ m, which add back to 1800 m.

Notes

Keep the units of speed and distance consistent. Speeds per minute give an answer in minutes, speeds per hour give an answer in hours.

This formula does not apply when both move the same way. Chasing someone ahead of you, the gap closes only by the difference in speed, which is a catching-up problem instead.

If the speeds add up to zero the gap never shrinks, so they never meet.