Train A and train B leave station going in opposite directions. Train B leaves 1/2 later than train A. Train B travels 80km/h faster than Train A. In 2 hours the trains are 3200KMs apart. How fast is each train traveling..
thank you
Let x = speed of A and x + 80 = speed of B.
Speed = distance/time. therefore
Distance = speed * time
Distance traveled by A + distance traveled by B = 3200
This should help you solve your problem. Thanks for asking.
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Homework Help Forum: Math
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Posted by Lucas on Tuesday, October 16, 2007 at 8:47pm.
Train A and train B leave station going in opposite directions. Train B leaves 1/2 later than train A. Train B travels 80km/h faster than Train A. In 2 hours the trains are 3200KMs apart. How fast is each train traveling..
thank you
The answer depends on whether the total elapsed time is 2 hours or 2.5 hours.
The statement "In 2 hours, the trains are 3200km apart" could mean 2 hours total elapsed time including the 1/2 hour head start of train A before train B departs or 2 hours of elapsed time "after" train A traveled 1/2 hour.
Let V = the speed of train A
Let V + 80 = the speed of train B
Assuming that the total travel time of both trains is 2 hours:
1--Train A travels distance d = .5V in 1/2 hour.
2--The travel time of train B is (3200 - .5V)/(2V + 80) = 1.5 hours
3--3200 - .5V = 3V + 120
4--3.5V = 3080 making V = 880 km/hr.
5--Train B's speed is therefore 960km/hr.
Check:
Train A travels 440km in the first 1/2 hour.
This results in 2760km between the two trains when train B departs.
They are seperating from one another at the combined speed of 880 + 960 = 1840KM/HR.
The time required for them to be 3200km apart at the end of 2 hours is t = 2760/1840 = 1.5 hours.
Total elapsed time is 1/2 + 1.5 = 2 hours.
To solve this problem, let's break it down step by step:
Step 1: Determine the time it takes for Train A to travel a certain distance.
Let's assume that Train A has been traveling for t hours when Train B starts. Since Train B leaves half an hour after Train A, the time it has been traveling is t - 1/2 hours.
To find the distance traveled by Train A in t hours, we can use the formula:
Distance = speed × time.
Since the speed of Train A is unknown, let's call it x km/h. Therefore, the distance traveled by Train A in t hours is x × t km.
Step 2: Determine the time it takes for Train B to travel the same distance.
Since Train B leaves half an hour after Train A, it has been traveling for t - 1/2 hours when the two trains are 3200 km apart. Therefore, the distance traveled by Train B in t - 1/2 hours is (x + 80) × (t - 1/2) km.
Step 3: Determine the total distance traveled by both trains.
In 2 hours, Train A and Train B are 3200 km apart. The distance traveled by Train A is x × 2 km, and the distance traveled by Train B is (x + 80) × (2 - 1/2) km. Adding these distances together gives us the total distance:
Distance_A + Distance_B = 3200 km.
Now we can solve the equation:
x × 2 + (x + 80) × (2 - 1/2) = 3200.
Simplifying the equation:
2x + (x + 80) × (3/2) = 3200,
2x + (3/2)x + 120 = 3200,
4x + 3x + 240 = 6400,
7x = 6160,
x = 880.
Therefore, Train A is traveling at a speed of 880 km/h, and Train B is traveling at a speed of 960 km/h.