A train leaves New York for Boston, 200 miles away, at 3:00 P.M. and averages 70 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 55 mph. At what time will the trains meet? (Round to the nearest minute.)
at time t hours after 3:00, the trains have gone
70t miles and 55(t-1) miles
when they meet,
70t + 55(t-1) = 200
Now, just find t and add it to 3:00
Tina 5:02:24
To find the time when the trains meet, we need to determine the time it takes for each train to reach the meeting point.
The first train leaves New York at 3:00 P.M. and travels for a certain amount of time until it meets the second train. Let's call this time 't'. Given that the speed of the first train is 70 mph and the distance to be covered is 200 miles, we can use the formula:
Distance = Speed × Time
200 = 70t
Now, let's find the time it takes for the second train to reach the meeting point. The second train leaves Boston at 4:00 P.M., which means it has already traveled for an hour when the first train starts. So, when the second train starts, it travels 't' hours until it meets the first train. Given that the speed of the second train is 55 mph and the distance to be covered is also 200 miles, we can use the same formula:
Distance = Speed × Time
200 = 55(t - 1)
Now we have a system of two equations:
1) 200 = 70t
2) 200 = 55(t - 1)
To solve this system, we can substitute equation 1 into equation 2:
200 = 55(70t - 1)
Now let's solve for 't':
200 = 3850t - 55
2455 = 3850t
t ≈ 0.64 hours (rounded to two decimal places)
To convert this to minutes, multiply by 60:
0.64 × 60 ≈ 38.4 minutes
So, the trains will meet approximately 38.4 minutes after the first train departs at 3:00 P.M.
Adding this time to the starting time, we find:
3:38.4 P.M. (rounded to the nearest minute)
Therefore, the trains will meet at approximately 3:38 P.M. (rounded to the nearest minute).