Solve each problem. A boat can travel 20 mi against a current in the same time that it can trave

step 1 Right. We are dealing with distance equals rate times time. So let's set up a little table here.

Solve each problem. A boat can travel 20 mi against a...

Solve each problem. A boat can travel $20 \mathrm{mi}$ against a current in the same time that it can travel $60 \mathrm{mi}$ with the current. The rate of the current is $4 \mathrm{mph}$. Find the rate of the boat in still water.

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Key Concepts

Relative Speed

Relative speed is the effective speed of an object when other motion influences, such as a current or wind, are present. It involves adding or subtracting the speed of the medium from the object's speed in still conditions, depending on the direction of travel relative to the medium.

Time Equivalence Principle

This principle involves setting equal the time taken for two or more different journeys when they are known to take the same duration. It is applied by relating distance and effective speed through the equation time = distance/speed.

Equation Setup

Setting up an equation in such problems requires expressing the travel time for each leg of the journey using distance and relative speed, then equating these expressions to solve for the unknown variable.

Algebraic Manipulation

This concept involves rearranging and simplifying equations, combining like terms, and isolating the desired variable to find a solution. It is a fundamental skill for solving linear equations that arise in motion problems.

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