Answer :
Final answer:
The slower bus travels at a speed of approximately 68 miles/hour and the faster bus travels at a speed of 81 miles/hour, considering that they are traveling in opposite directions.
Explanation:
This problem deals with the concept of relative speed. Given two buses are traveling in opposite directions, their speeds would be added. Let's assume the speed of the slower bus is x (miles/hour). Therefore, the speed of the faster bus would be x+13 (miles/hour).
After 6 hours, they are 894 miles apart. So, x (speed of slower bus) multiplied by 6 (hours) plus x+13 (speed of faster bus) multiplied by 6 (hours) equals 894 miles. This forms the equation: 6x + 6(x+13) = 894.
To solve this equation, combine like terms to get 12x + 78 = 894, then subtract 78 from both sides to get 12x = 816. To get x, divide both sides by 12 to obtain x ≈ 68 miles/hour. Hence, the slower bus travels around 68 miles/hour and the faster bus travels at 68+13 = 81 miles/hour.
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The slower bus travels at a speed of 68 mi/h.
The faster bus travels at a speed of 81 mi/h.
To solve this problem, let's define the speed of the slower bus as [tex]x \, \text{mi/h}[/tex]. Since the other bus travels 13 mi/h faster, its speed will be [tex]x + 13 \, \text{mi/h}[/tex].
The two buses are traveling in opposite directions. After 6 hours, the total distance between them is given as 894 miles.
Write the equation:
Since distance is velocity multiplied by time, for the slower bus, the distance is:
[tex]\text{Distance}_{\text{slower}} = x \times 6 = 6x[/tex]
And for the faster bus, the distance is:
[tex]\text{Distance}_{\text{faster}} = (x + 13) \times 6 = 6(x + 13)[/tex]
The total distance apart is given by:
[tex]6x + 6(x + 13) = 894[/tex]
Simplify the equation:
Distribute and simplify the terms:
[tex]6x + 6x + 78 = 894[/tex]
Combine like terms:
[tex]12x + 78 = 894[/tex]
Subtract 78 from both sides:
[tex]12x = 816[/tex]
Finally, solve for [tex]x[/tex]:
[tex]x = \frac{816}{12} = 68[/tex]
So, the speed of the slower bus is 68 mi/h.
Determine the speed of the faster bus:
Since the faster bus travels 13 mi/h faster than the slower bus:
[tex]x + 13 = 68 + 13 = 81[/tex]
Therefore, the speed of the faster bus is 81 mi/h.