4. A train travels from Town A to Town B at an average speed of 50 miles per hour and makes the return trip at an average speed of 60 miles per hour. If the total time for the round trip is 11 hours, what is the distance between Town A and Town B?

Let the distance between Town A and Town B be d miles.

For the trip from Town A to Town B, the time it takes is d/50 hours.

For the return trip, the time it takes is d/60 hours.

The total time taken for both trips is 11 hours, so we have the equation:

d/50 + d/60 = 11

To solve this equation for d, first multiply each side by the least common multiple (LCM) of 50 and 60, which is 300:

300(d/50 + d/60) = 300 * 11

Simplifying and combining terms gives us:

6d + 5d = 3300

11d = 3300

Now, divide both sides by 11 to find the value of d:

d = 3300 / 11 = 300

So, the distance between Town A and Town B is 300 miles.