SOLUTION: a steamboat travels 14 km/h faster than a freighter. the steamboat travels 84km in the same time the freighter travels 49 km. what is the speed of each boat?

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Question 247794: a steamboat travels 14 km/h faster than a freighter. the steamboat travels 84km in the same time the freighter travels 49 km. what is the speed of each boat?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the speed of the freighter. Then is the speed of the steamboat. Let represent the common amount of time.

We know that distance equals rate times time, , but this can be solved for :

Now we can describe the freighter's trip like this:

And we can describe the steamboat's trip like this:

Now we have two expressions that are both equal to , so set them equal to each other:

Now all you need to do is cross-multiply and solve for . Let me know what you get for an answer.

John

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a steamboat travels 14 km/h faster than a freighter. the steamboat travels 84km in the same time the freighter travels 49 km. what is the speed of each boat?
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Freighter DATA:
rate = x km/h ; distance = 49 km ; time = d/r = 49/x hrs
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Steamboat DATA:
rate = x+14 km/h ; distance = 84 km ; time = d/r = 84/(x+14) hrs
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Equation:
time = time
49/x = 84/(x+14)
84x = 49(x+14)
84x = 49x + 49*14
35x = 48*14
x = 19.2 km/h (speed of the freighter)
x+14 = 33.2 km/h (speed of the steamboat)
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Cheers,
Stan H.