Question 201570: A ship went up a stream of 36km in 3 hours, and went down the same distance in 2 hours. What is the km per hour for this ship if there is no speed in this stream? What is this stream's km per hour?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ship is travelling at 15 kilometers per hour.
the stream is travelling at 3 kilometers per hour.
here's how to figure it out.
let x = speed of ship.
let y = speed of water.
rate and speed mean the same thing, at least here.
general formula is rate times time = distance.
you can also say speed times time = distance.
ship and boat mean the same thing here also.
going with the current of the water, the rate of speed of the water adds to the rate of speed of the boat.
going against the current of the water, the rate of speed of the water detracts (subtracts) from the speed of the boat.
so, going with the current of the water, the rate of the boat and the water is x + y, and going against the current of the water, the rate of the boat and the water is x - y.
since rate times time = distance, we have:
3 (x-y) = 36 which is going against the current of the water.
and we have
2 (x + y) = 36 which is going with the current of the water.
since they both equal 36, then they are equal to each other so we have
3 * (x-y) = 2 * (x + y)
removing parentheses, we get
3x - 3y = 2x + 2y
subtracting 2x from both sides and adding 3 y to both sides, we get
x = 5y
this means that the rate of the boat is 5 times the rate of the water.
now that we know one of the unknowns, we can solve for the other.
take either equation and solve for y.
using 2 * (x + y) = 36, and replacing x with 5y, we get
2 * (5y + y) = 36
which becomes
2 * 6y = 36
which becomes
12 * y = 36
which becomes
y = 3
so, the rate of the water is 3 km per hour.
since the boat is 5 times this, then the rate of the boat is 15 kmph.
making x = 15 and y = 3, and substituting in the other equation, we get
3 * ( x-y) = 36
becomes
3 * (15-3) = 36
becomes
3 * (12) = 36
becomes
36 = 36
answer is true so the values are good.
answer is:
rate of the ship is 15 kmph
rate of the water is 3 kmph
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