TRAIN A, TRAVELING 70 MPH, LEAVES WESTFORD HEADING TOWARD EASTFORD 260 MILES AWAY. AT THE SAME TIME TRAIN B TRAVELING 60 MPH, LEAVES EASTFORD HEADING TOWARD WESTFORD. WHEN DO THE TWO TRAIN MEET? HOW FAR FROM EACH CITY DO THEY MEET? SHOW OR EXPLAIN HOW YOU GOT YOUR ANSWER.

To find when and where the two trains meet, we can use the formula:

Time = Distance / Speed

Let's start by finding the time it takes for Train A to reach the meeting point.

Time for Train A = Distance / Speed = 260 miles / 70 mph ≈ 3.71 hours

Now, let's find the time it takes for Train B to reach the meeting point.

Time for Train B = Distance / Speed = 260 miles / 60 mph ≈ 4.33 hours

Since the two trains started at the same time, we need to find the average time it takes for them to meet.

Average time = (Time for Train A + Time for Train B) / 2
Average time = (3.71 hours + 4.33 hours) / 2 ≈ 4.02 hours

Now, we can find the distance from each city that they meet.

Distance from Westford = Speed of Train A × Average time = 70 mph × 4.02 hours ≈ 281.4 miles

Distance from Eastford = Speed of Train B × Average time = 60 mph × 4.02 hours ≈ 241.2 miles

Therefore, the two trains will meet approximately 4.02 hours after they both start traveling. They will meet around 281.4 miles from Westford and 241.2 miles from Eastford.

To find out when the two trains will meet and how far from each city they will meet, we can use the concept of relative motion. Let's break down the problem step by step:

1. Determine the time it takes for the trains to meet:
Since Train A is traveling at 70 mph and Train B is traveling at 60 mph, the combined speed of the two trains is 70 mph + 60 mph = 130 mph.

Distance = Speed × Time
260 miles = 130 mph × Time
Time = 260 miles / 130 mph
Time = 2 hours

Therefore, it will take 2 hours for the two trains to meet.

2. Calculate the distance each train has traveled when they meet:
Since Train A is traveling at 70 mph for 2 hours, it will cover a distance of 70 mph × 2 hours = 140 miles.

Similarly, since Train B is traveling at 60 mph for 2 hours, it will cover a distance of 60 mph × 2 hours = 120 miles.

3. Determine the distance from each city where they meet:
Since Train A has traveled 140 miles and Train B has traveled 120 miles when they meet, we need to find the remaining distance from each city.

From Westford:
Distance from Westford = Total distance - Distance covered by Train A
Distance from Westford = 260 miles - 140 miles = 120 miles

From Eastford:
Distance from Eastford = Total distance - Distance covered by Train B
Distance from Eastford = 260 miles - 120 miles = 140 miles

Therefore, the trains will meet 120 miles away from Westford and 140 miles away from Eastford.

To summarize:
- The two trains will meet after 2 hours.
- They will meet 120 miles away from Westford and 140 miles away from Eastford.

This solution was found by using the formula D = ST to determine the time each train will travel, and then subtracting the distances covered from the total distance to find the distances from each city where they meet.