# Math

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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

• Math -

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

• Math -

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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.