A train going 60 mph left several minutes before the 63mph train. Traveling on parallel tracks the faster train reaches the slower one in 3 hours. How many minutes head start did the slower train have?
Both trains had traveled the same distance:
d1 = d2.
60t = 63*3 = 189 mi.
t = 3.15h.
3.15h - 3h = 0.15h = 9min head start.
To find the head start of the slower train in minutes, we need to convert the time from hours to minutes.
Let's start by calculating the distance traveled by the slower train in 3 hours:
Distance = Speed × Time
Distance = 63 mph × 3 hours = 189 miles
Since the faster train catches up with the slower train, their travel distances are the same. Therefore, the slower train travels 189 miles in 3 hours.
Now, let's calculate the time taken by the slower train to cover this distance at its speed of 60 mph:
Time = Distance / Speed
Time = 189 miles / 60 mph
We need to convert this time from hours to minutes. Since 1 hour is equal to 60 minutes, we can multiply the time by 60:
Time in minutes = (189 miles / 60 mph) × 60 minutes/hour
Calculating this, we get:
Time in minutes = (189 miles / 60) × 60 minutes = 189 minutes
Therefore, the slower train had a head start of 189 minutes.
To find out the head start in minutes that the slower train had, we need to understand the concept of relative speed.
Relative speed is the difference between the speeds of two objects moving in the same direction. In this case, the faster train is moving at 63 mph, and the slower train is moving at 60 mph. Therefore, the relative speed is the difference between the two speeds: 63 mph - 60 mph = 3 mph.
Given that the faster train catches up to the slower train in 3 hours, we can now calculate the head start the slower train had by using the formula:
Head start = Relative speed * Time
Plugging in the values, we get:
Head start = 3 mph * 3 hours
Multiplying 3 mph by 3 hours, we get:
Head start = 9 miles
So, the slower train had a head start of 9 miles.
To convert this head start into minutes, we need to know the time it takes for both trains to travel 1 mile. Since we are given the speeds in miles per hour (mph), we need to determine the time it takes for each train to travel 1 mile.
For the slower train traveling at 60 mph, it takes 60 minutes to travel 1 mile.
Now, we can calculate the head start in minutes by using the formula:
Head start in minutes = Head start (in miles) * Time (in minutes per mile)
Plugging in the values, we get:
Head start in minutes = 9 miles * 60 minutes per mile
Multiplying 9 miles by 60 minutes per mile, we get:
Head start in minutes = 540 minutes
Therefore, the slower train had a head start of 540 minutes.