If car 1 took 2.05 second to travel 1 tile, and car 2 took .7 seconds to travel 1 tile, at what point in the room would the cars collide if they were traveling at opposite directions. There are 31 total tiles.

I'm not asking for an answer but just how to go about solving this. Would there be a formula to solve it or just multiplying to cancel units?

## Answers (1)

Distance = Number of tiles

Velocity = Number tiles ÷ time

Car 1, v1 = 1/ 2.05 tile/s, d1 = 1/ 2.05 * t

Car 2, v2 = 1/0.7, d2 = 1/0.7 * t

The sum of these two distances is 31 tiles

1/ 2.05 * t + 1/0.7 * t = 31

Multiply both sides by 2.05 * 0.7

0.7 * t + 2.05 * t = 44.485

2.75 * t = 44.458

t = 44.485/2.75

Use the time to determine the distance each car traveled.

d1 = 1/ 2.05 * 44.485/2.75 ≈ 7.89

d2 = 1/0.7 * 44.845/2.75 ≈ 23.1

The car’s collided when at point which is approximately 7.9 tiles from car 1’s initial position. I do not think I could have explained how solve this problem without numbers.