Question 1089693: I am having difficulty deciphering and solving the following question. I'm sure I'm over complicating it, but I don't quite understand.
"You'll be traveling on the steamboat and the tall ship. The steamboat makes the trip in 5 hours. The tall ship makes the trip in 10 hours. The tall ship is 10 knots slower than the steamboat. For each boat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?"
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52884)   (Show Source):
You can put this solution on YOUR website! .
Your equation is
5x = = 10*(x-10),
where x is the speed (the rate) of the steamboat, in knots.
It says that the distances traveled by each ship are the same.
Simplify and solve for x:
5x = 10x - 100 ====> 100 = 10x - 5x ====> 5x = 100 ====> x =  = 20 knots.
Answer. Steamboat speed is 20 knots. The tall ship speed is 20-10 = 10 knots.
Please check on your own that the solution is correct.
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Lots of wording to give you a hint, and information that is not essential.
People figuring out their own trips know that speed is distance covered per unit time.
You measure distance in your preferred units,
and divide it by the corresponding time in your preferred units.
Conversely, if you know the speed and time, you multiply them together to find the distance traveled. The wording of the problem tells you that, just in case.
Adults who did not study algebra do those calculations in the real life.
Student life is not real enough.
People use different units, and may end up with speeds in meters per second, miles per hour, or nautical miles per hour.
I did not know that nautical miles per hour are called knots. It's nice to know, but not needed to solve the problem.
 = speed of the steamboat, in boots (I am defining a variable).
 = speed of the tall ship, in knots (The problem says so).
The problem tells you the travel time for your trips (5 hours on the steamboat, and 10 hours on the tall ship), so
 = time × speed (= distance) for the steamboat trip.
 = time × speed (= distance) for the tall ship trip.
The problem tells you that those two distances are the same, so
 is the equation to solve.
Can you solve it? If you can, do it (without peaking at the solution I shoe below).
The units for speed and time were the same for both trips,
so we did not need to know what "hour" and "knot" mean,
or what units were used to measure the distance.
MY SOLUTION
 .
So,  .
The steamboat is traveling at 20 knots, and the tall ship is traveling at 10 knots.
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