Question 243381: A plane travel 100 kph faster than a train the plane covers 500 km in the same time that train coves 300 km find the speed of each one?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Always be careful to define your variables and equations with the fewest possible unknowns. That usually means defining variables in terms of one other wherever possible.
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In this case, we could say the speed of the plane is 'x' and that the speed of the train is 'x - 100', which means it is 100 mph slower. OR we could say the train's speed is 'x' and the plane's speed = 'x + 100'.
Pick either one you prefer.
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Distance and rate problems are common in algebra. Remember the fundamental equation is:
distance = rate * time
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The plane's characteristics are:
d = 500 km
r = x
t = same time as the train
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The train's characteristics are:
d = 300 km
r = x - 100
t = same time as plane
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Since the one thing that is equal is time, we can format each equation to isolate t.
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For the plane:
t = d/r
t = 500/x
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For the train:
t = d/r
t = 300/(x-100)
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Now we can rely on the principle that if a=b and b=c, then a=c. Or "equals are equal."
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500/x = 300/(x-100)
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Now we can cross-multiply
500 * (x-100) = 300 * x
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Multiplying through on the left we have
500x - 50,000 = 300x
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Subtracting 300x from both sides
200x -50,000 = 0
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Adding 50,000 to both sides
200x = 50,000
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Dividing both sides by 200
x = 250
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Looking back at the setup, the train's speed is 250 - 100 = 150.
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Now we need to check our work.
How long does it take for the plane to travel 500 km? 2 hrs @ 250 km/hr
How long does it take the train to travel 300 km? 2 hrs @ 150 km/hr
So, we're confident in our answer:
The plane's speed is 250 km/hr, and the train's speed is 150 km/hr.
Done.
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