# A boat goes 50 miles upstream in 3 hours and later returns to the starting point in 2 hours. What is the speed of the boat in still water and what is the speed of the current?

The boat's speed is **20 5/6 mph**, and the river's speed is
**4 1/6 mph**. Here's how we solve it: In going upstream, the
boat moves against the river's current, so the speed of the current
is subtracted from the speed of the boat. The opposite it true for
it travel downstream, because in that instance, the speed of the
river is added to the speed of the boat. If we us B as the speed of
the boat and R as the speed of the river, then in moving upstream
50 miles in 3 hours, 3 times the boat's speed minus 3 times the
river's speed is 50 miles. Downstream, the 50 mile trip took 2
hours, so 2 times the boat's speed plus 2 times the river's speed
is 50 miles. Here are the equations. 3B - 3R = 50 2B + 2R = 50 When
we have two unique equations, which we have, that contain two
variables, which we also have (the speed of the boat and the speed
of the river), we can solve by the method of simultaneous
equations. In this method, we "add" the two equations together
algebraically. Our goal in this, however, must be to make one of
the variable "drop out" or "cancel out" so that only one variable
remains. If we multiply the first equation by 2 and the second
equation by 3, we'll end up with a "-6R" term in the first
equation, and a "+6R" term in the second equation. When these two
terms are added algebraically, they'll "disappear" and leave a
single variable in the resulting equation. Let's multiply as we
suggested. 2 (3B - 3R = 50) = 6B - 6R = 100 3 (2B + 2R = 50) = 6B +
6R = 150 Adding the two equations together algebraically will now
make one term "go away" and we can solve for the other variable.
Here's how it looks when we add: (6B + 6B) + (-6R + 6R) = (100 +
150) 12B = 250 [Notice that the R term has "cancelled out" and we
are left with one variable.] Solving for B, the speed of the boar,
we have this: 12B = 250 B = 20 5/6 miles per hour Returning with
that to one equation, we can solve for the other variable. Let's
plug it into the second equation. 2B + 2R = 50 2(20 5/6) + 2R = 50
41 2/3 + 2R = 50 2R = 50 - 41 2/3 2R = 8 1/3 R = 4 1/6 mph [This is
the speed of the river's current.] Let's check by substituting both
answer back into the first equation. 3B - 3R = 50 3(20 5/6) - 3(4
1/6) = 50 (62 1/2) - (12 1/2) = 50 50 = 50 [Our work checks, and
the speeds of the boat and current are correct. Note that we could
have arrived at the same answer by multiplying the first equation
through by -2 and getting -6B + 6R = -100, and then multiplying the
second equation through by 3 and getting 6B + 6R = 150 for our two
equations. Then adding them algebraically, we get 12R = 50 and our
B term has dropped out. Solving for this to find the speed of the
current we get R = 4 1/6 mph, which is identical to what we got
when we worked it through the first time.

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### A person can row downstream 20km in 2 hours and upstream 4km in 2 hours. find the speed of the current?

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It will depend on where you are starting from, but it is at least 2 hours. It will depend on where you are starting from, but it is at least 2 hours. It will depend on where you are starting from, but it is at least 2 hours. It will depend on where you are starting from, but it is at least 2 hours. It will depend on where you are starting from, but it…

### If a boat travels upstream against a 3 mph current and travels 5 hours and the return trip takes 2.5 hours what is the speed of the boat?

Suppose the speed of the boat is x mph. Then upstream, it travels 5 hours at x-3 mph and so covers 5x - 15 miles. When going downstream the boat covers the same distance, at x+3 mph, in 2.5 hours so (5x-15)/(x+3) = 2.5 Multiply through by 2*(x+3): 2*(5x-15) = 5*(x+3) 10x - 30 = 5x + 15 or 5x = 45 giving x = 9 mph.

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The sun moves across the sky and returns to its starting point in 24 hours. So does the background star field. It is highly unlikely that these two things would happen with exactly the same frequency if it were them which were moving. It is much more sensible to believe that they stay still and our planet spins once in 24 hours.

### If Tina swims 4 miles upstream at 1 mph and back downstream to the same point at 4 mph what is her average speed?

Her average speed is 1.6 miles per hour. Average speed is total distance covered by total time taken to do it. She swims 4 miles upstream, and at 1 mph, it takes 4 hours. She comes back downstream at 4 mph and so she covers the 4 miles in 1 hour. Her total mileage is 8 miles. It takes 4 + 1 hours or 5 hours to cover it. The 8 miles divided by 5…