A boat moves 7 kilometers upstream in the same amount of time it moves 17 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
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To find the rate of the boat in still water, we need to set up an equation using the given information.
Let's assume the rate of the boat in still water is represented by 'b' km/h.
When the boat moves upstream (against the current), the effective speed is reduced by the speed of the current. So the boat's speed is (b - 9) km/h.
When the boat moves downstream (with the current), the effective speed is increased by the speed of the current. So the boat's speed is (b + 9) km/h.
Now we can use the formula: distance = speed × time.
Given that the boat moves 7 kilometers upstream and 17 kilometers downstream in the same amount of time, we have two equations:
7 = (b - 9) × t
17 = (b + 9) × t
Since the time is the same in both cases, we can set the left-hand sides of the equations equal to each other:
7 = (b - 9) × t = (b - 9) × (17/b) (substituting t by 17/b since t is the same in both cases)
Simplifying this equation, we get:
7b = 17(b - 9)
Now let's solve the equation:
7b = 17b - 153
10b = 153
b = 153/10
Therefore, the rate of the boat in still water is 15.3 km/h.