Question
A train leaves Boston and travels towards its destination at a speed of 60mph. One hour later, an express train leaves Boston and travels towards the same destination at a speed of 80mph. How far away from Boston is their destination if they arrive at the same time.
Answers
GPT 3.5
Let d be the distance to the destination.
Since the first train traveled for one hour longer than the second train, we can express the time taken by the first train as (d/60) + 1 and by the second train as d/80.
Given that they arrive at the same time, we have the following equation:
(d/60) + 1 = d/80
Multiplying through by 240 (the least common multiple of 60 and 80), we get:
4d + 240 = 3d
Solving for d, we get:
d = 240
Thus, the destination is 240 miles away from Boston.
Since the first train traveled for one hour longer than the second train, we can express the time taken by the first train as (d/60) + 1 and by the second train as d/80.
Given that they arrive at the same time, we have the following equation:
(d/60) + 1 = d/80
Multiplying through by 240 (the least common multiple of 60 and 80), we get:
4d + 240 = 3d
Solving for d, we get:
d = 240
Thus, the destination is 240 miles away from Boston.