Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 16 faster than the other. If the two buses are 592 miles apartafter 4 hours, what is the rate of each bus?

Answer 1

Step-by-step explanation:

Let's call x the rate of the first bus and y the rate of the second bus.

If one bus travels 16 miles per hour faster than the other, we can write the following equation:

y = x + 16

On the other hand, the distance travel by each bus after 4 hours can be calculated as 4 times the rate. So, 4x is the distance travel by the first bus and 4y is the distance traveled by the second bus. If after 4 hours, they are 592 miles apart, we can say that:

4x + 4y = 592.

Now, we can replace the first equation y = x + 16 into the second equation as follows:

4x + 4y = 592

4x + 4(x + 16) = 592

Solving for x, we get:

4x + 4(x) + 4(16) = 592

4x + 4x + 64 = 592

8x + 64 = 592

8x + 64 - 64 = 592 - 64

8x = 528

8x/8 = 528/8

x = 66

Now, we can calculate the value of y as:

y = x + 16

y = 66 + 16

y = 82

Therefore, the rate of the first bus is 66 miles per hour and the rate of the second bus is 82 miles per