Answer:
The speed of the boat in still water is 12 miles per hour, while the speed of the current is 9 miles per hour.
Explanation:
We'll use x as the speed of the boat in still water in miles per hour.
We'll use y as the speed of the current in miles per hour.
When the boat is traveling downstream, the speed of the boat is helped by the speed of the current and the net speed is x + y.
When the boat is traveling upstream, the current opposes the movement of the boat, and the net speed is x - y.
Using a table where d = distance in miles, r = rate or speed in miles per hour, and t = time in hours can help figure out how to figure out this problem.
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Downstream│210│(x + y)│10
Upstream│210│(x - y)│70
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Recall that distance = rate x time or d = rt.
210 = (x + y)10 ➤ Equation from downstream information.
210 = (x - y)70 ➤ Equation from downstream information.
210 = 10x + 10y ➤ Distribute.
210 = 70x - 70y ➤ Distribute.
7 × 210 = 7 × 10x + 7 × 10y ➤ Multiply the 1st equation by 7.
1470 = 70x + 70y ➤ Add the 1st equation to the 2nd.
210 =70x - 70y ➤ Add the 1st equation to the 2nd.
1680 = 140x
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1680/140 = 140x/140
x = 12
210 = (12 + y)10 ➤ Substitute x = 12 into one of the original equations to find y.
210 = 120 + 10y
-120 - 120
90 = 10y
90/10 = 10y/10
y = 9