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A motorboat left a harbor and traveled at an average speed of $15\,\text{mph}$ toward an island. The average speed on its return trip was $10\,\text{mph}$ . How far was the island from the harbor if the total trip took $5$ hours?

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Identify quotients of rational numbers: word problems

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Q. A motorboat left a harbor and traveled at an average speed of

15\,\text{mph}

toward an island. The average speed on its return trip was

10\,\text{mph}

. How far was the island from the harbor if the total trip took

5

hours?

Set up equation: Let's denote the distance to the island as $d$ miles. The time to travel to the island is $\frac{d}{15}$ hours, and the time for the return trip is $\frac{d}{10}$ hours. The total time for both trips is $5$ hours. Set up the equation: $\newline$ $\frac{d}{15} + \frac{d}{10} = 5$
Find common denominator: To solve for $d$ , find a common denominator for the fractions, which is $30$ . Rewrite the equation: $\newline$ $\frac{2d}{30} + \frac{3d}{30} = 5$
Combine terms: Combine the terms on the left side: $\newline$ $\frac{5d}{30} = 5$
Simplify equation: Simplify the equation by multiplying both sides by $30$ : $\newline$ $5d = 150$
Divide to solve: Divide both sides by $5$ to solve for $d$ : $\newline$ $d = 30$

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