07 - A Man Covers an Unknown Distance at Different Rates | College Algebra Review at MATHalino

Problem
A man covers the distance A to B in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from B to A, by traveling 1 km/hr faster than during the first half of his trip from A to B, he consumed 3-3/4 hours. Determine the distance AB.

Answer Key

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15 km

Solution

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Let
x = distance between A and B in kilometer
v = original velocity (velocity during the 1st half of the distance AB)

From A to B
$\dfrac{0.5x}{v} + \dfrac{0.5x}{v - 0.5} = 5.5$ ← Equation (1)

From B to A
$\dfrac{x}{v + 1} = 3.75$

$v = \dfrac{x}{3.75} - 1$

From Equation (1)
$\dfrac{0.5x}{\dfrac{x}{3.75} - 1} + \dfrac{0.5x}{\left( \dfrac{x}{3.75} - 1 \right) - 0.5} = 5.5$

$x = 15 ~ \text{km}$ answer

07 - A Man Covers an Unknown Distance at Different Rates

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