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Going against the current, a boat takes 6 hours to make a 120 -mile trip. When the boat travels with the current on the return trip, it takes 5 hours. What is the rate of the boat in still water? 2 mph 22 mph 20 mph

Ask by Gray Norton. in the United States
Feb 27,2025

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The boat's speed in still water is 22 mph.

Solución

Let x be the speed of the boat in still water and y be the speed of the current. When the boat is going upstream (against the current), its effective speed is x - y. Given that it takes 6 hours to cover 120 miles:   x - y = 120 miles / 6 hours = 20 mph. When the boat is going downstream (with the current), its effective speed is x + y. It takes 5 hours to cover the same 120 miles:   x + y = 120 miles / 5 hours = 24 mph. Now, we have the system of equations:   1. x - y = 20   2. x + y = 24 Adding the two equations eliminates y:   ( x - y ) + ( x + y ) = 20 + 24   2x = 44   x = 44 / 2 = 22 mph. Thus, the rate of the boat in still water is 22 mph.

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Beyond the Answer

To tackle this problem, let’s break it down! When the boat is going against the current, it has to fight against the water, making its effective speed slower. If we call the boat's speed in still water "b" and the current's speed "c," the equation for the trip against the current (120 miles) is: **b - c = 20 mph** (since 120 miles / 6 hours = 20 mph). On the return trip with the current, the effective speed becomes faster: **b + c = 24 mph** (120 miles / 5 hours = 24 mph). Solving these two equations gives us the boat's speed in still water: **b = 22 mph**! So, pack your bags, because this boat isn't just floating around! To avoid confusion with similar problems, ensure you clearly define your variables. Remember that the speed of the current can affect your effective traveling speed! Always write down your equations, double-check your calculations, and don’t forget to convert time as needed. A little bit of organization can lead you to victory!

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