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Basic Math/algebra word problem

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Expert: Josh - 5/26/2005


Question
a sailboat is 3 hours on the water before it reduces its average speed by 5 mph. It travels 57 miles in a total of 6 hrs. What was the speed during both segments?

Can you set that up as an equation for me and show me how it is worked out?

thank you

Answer
Let the unknown quantity be x.
Here, x represents the speed of the sailboat in the first three hours (from t=0 to t=3).
In the next three hours, the speed is 5 mph slower than before. So, from t=3 to t=6, its speed is given by (x-5) mph.

Distance travelled = speed * elapsed_time.

From t=0 to t=3, the distance travelled is given by "3x".
From t=3 to t=6, the distance travelled is given by "3(x-5)"

So, the total distance travelled,
57 = 3x + 3(x-5) = 6x-15.
Solving for x, x=(57+15)/6 = 12 mph.

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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