Solving a distance, rate, time problem using a system of linear

Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 16km/h slower than the other. If the two buses are 786 kilometers apart after 3 hours, what is the rate of each bus?

Answer 1

The total distance covered by the two buses is given as 786 kilometers.

So, we can write the equation: 3x + 3(x - 16) = 786

Simplifying the equation: 3x + 3x - 48 = 786 6x - 48 = 786 6x = 786 + 48 6x = 834 x = 834 / 6 x ≈ 139

Therefore, the rate of the faster bus is approximately 139 km/h, and the rate of the slower bus is 139 - 16 ≈ 123 km/h.