Question

Solving a distance, rate, time problem using a system of linear.... 015 Jessica V h Two buses leave a station at the same time and travel in opposite directions. One bus travels 15 faster than the other. If the two buses are 246 miles apart after 2 hours, what is the rate of each bus? ​

Answer 1

Answer: Therefore, the rate of the slower bus is 54 mph, and the rate of the faster bus is 69 mph.

Step-by-step explanation: Let's use the following variables to represent the rates of the two buses:

- Let x be the rate of the slower bus

- Then, x + 15 is the rate of the faster bus

Using the formula: Distance = Rate * Time

After 2 hours, the distance traveled by the slower bus is:

Distance = Rate * Time

Distance = x * 2

And the distance traveled by the faster bus is:

Distance = Rate * Time

Distance = (x + 15) * 2

The sum of the distances is equal to 246 miles:

Distance of slower bus + Distance of faster bus = 246

2x + 2(x + 15) = 246

Solve for x:

2x + 2x + 30 = 246

4x = 216

x = 54

Therefore, the rate of the slower bus is 54 mph, and the rate of the faster bus is 69 mph.