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Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 miles per hour faster than the other. The two buses are 768 miles apart after six hours. What is the rate of each bus?

Answer :

Two buses leave a station at the same time and travel in opposite directions. After six hours, the two buses are 768 miles apart. We find that the speed of the first bus is 57 miles per hour, and the speed of the second bus is 71 miles per hour.

Let the speed of one bus be x miles per hour. Then the speed of the other bus is (x+14) miles per hour, as it travels 14 miles per hour faster.

We know that the two buses travel in opposite directions and are 768 miles apart after six hours. Using the formula:

Distance = Speed x Time

we can write two equations:

Distance covered by the first bus = x * 6

Distance covered by the second bus = (x+14) * 6

The sum of these distances is equal to 768 miles:

x * 6 + (x+14) * 6 = 768

Simplifying the equation, we get:

12x + 84 = 768

12x = 684

x = 57

Therefore, the speed of the first bus is 57 miles per hour, and the speed of the second bus is (57+14) = 71 miles per hour.

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