Train A leaves Romeoville at 8:00 am traveling at 55 mph toward Julietteville. Train B leaves Julietteville at the same time heading toward Romeoville at 35 mph. If the distance betweent the two towns is 337.5, what time do the two trains pass each other?
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Main concept: when they pass each other , each will have travelled the same time
distance covered by train A --- x
distance covered by train B --- 337.5 - x
time for A = x/55
time for B = (337.5-x)/35
x/55 = (337.5-x)/35
cross-multiply, solve for x, then find x/55
To find the time when the two trains pass each other, we need to consider the distance they travel relative to their speeds.
Let's first determine the time it takes for each train to reach the meeting point:
For Train A:
Since Train A is traveling at 55 mph, we can say it covers a distance of 55 miles in 1 hour. Therefore, it will cover half the distance (337.5/2 = 168.75 miles) in 168.75/55 hours.
For Train B:
Similarly, Train B is traveling at 35 mph, so it will cover a distance of 35 miles in 1 hour. It will also cover half the distance (168.75 miles) in 168.75/35 hours.
Now, to find the total time, we add the times it takes for each train to reach the meeting point:
Time = (168.75/55) + (168.75/35)
To convert this total time into hours and minutes, we can perform the calculations:
Time = (168.75/55) + (168.75/35) = 3.0682 + 4.8214 ≈ 7.8896
The trains pass each other approximately 7.8896 hours after they depart, or 7 hours and 53 minutes.
Since the trains leave at 8:00 am, we can calculate the passing time by adding 7 hours and 53 minutes to the departure time:
8:00 am + 7 hours 53 minutes ≈ 3:53 pm
Therefore, the two trains pass each other around 3:53 pm.