a freight train that is 1 mile long is traveling at 60mph. a second train that is 2 miles long is traveling 40mph. the trains are moving in opposite directions on parallel tracks. how many seconds does it take between the time their locomotives meet and their cabooses fully pass each other?

relative velocity=100mi/hr

distance: 2 miles

timeinhrs= distance/velocity convert that to seconds.

wouldnt the distance be 3 miles though if the one mile train must travel 1 mile (distance of itsself) plus the distance of the other train which is 2 miles?

1.8 minutes

To find the time it takes between the locomotives meeting and the cabooses fully passing each other, we need to determine how far the cabooses travel after the meeting point.

Let's break down the problem step by step:

Step 1: Calculate the distance the first train travels before the locomotives meet.
Since the first train is traveling at a speed of 60 mph and the distance it needs to cover before the locomotives meet is equal to the length of the second train (2 miles), we can use the formula:

Distance = Speed × Time

2 miles = 60 mph × Time

Simplifying the equation, we have:

Time = 2 miles / 60 mph

Step 2: Determine the remaining distance the cabooses need to travel after the locomotives meet.
Since the first train is 1 mile long and the second train is 2 miles long, the total distance the cabooses need to travel after the locomotives meet is 1 + 2 = 3 miles.

Step 3: Calculate the time it takes for the cabooses to pass each other.
The combined speed of the two trains is the sum of their individual speeds, given as 60 mph and 40 mph. Thus, their combined speed is 60 mph + 40 mph = 100 mph.

Using the formula:

Time = Distance / Speed

Time = 3 miles / 100 mph

Converting 3 miles to feet (since we are calculating time in seconds), we get:

Time = 3 miles × 5280 feet/mile = 15,840 feet / 100 mph

Step 4: Convert the time to seconds.
To convert time to seconds, we need to multiply by the conversion factor of 3600 seconds per hour:

Time = (15,840 feet / 100 mph) × (1 hour / 3600 seconds)

Time = (15,840 feet / 100 mph) × (1 / 3600) hours × (5280 feet / 1 mile) × (1 mile / 5280 feet) × (3600 seconds / 1 hour)

Simplifying the equation, we have:

Time = 15,840 / 100 × 1 / 3600 × 5280 / 1 × 1 / 5280 × 3600

This simplifies to:

Time = 15,840 / 360,000

Finally, we perform the division:

Time = 0.044

Therefore, it takes approximately 0.044 seconds between the time their locomotives meet and their cabooses fully pass each other.