The Train Trouble Problem
A train leaves London at 10:15 a.m. and travels to Manchester at a constant speed of 60 miles per hour. Another train leaves Manchester at 11:00 a.m. and travels toward London at a speed of 75 miles per hour. The distance between London and Manchester is 300 miles.
At what time will the two trains pass each other?
Step 1: Let’s figure out how far the first train travels before the second train starts
ReplyDeleteFrom 10:15 a.m. to 11:00 a.m. = 45 minutes = 0.75 hours
In that time, the first train travels:
60 miles/hour × 0.75 hours = 45 miles
So when the second train starts at 11:00 a.m., the first train has already covered 45 miles.
That means the distance between the two trains at 11:00 a.m. is 300 - 45 = 255 miles.
Step 2: Now, both trains are moving toward each other
Their combined speed = 60 + 75 = 135 miles/hour
Now we calculate the time taken to meet after 11:00 a.m.:
255 miles ÷ 135 miles/hour = 1.888... hours
Convert 0.888... hours to minutes:
0.888 × 60 ≈ 53.3 minutes
So they meet 1 hour and 53 minutes after 11:00 a.m.
⇒ Time of meeting = 11:00 a.m. + 1 hour 53 minutes = 12:53 p.m.