07 - A Man Covers an Unknown Distance at Different Rates

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

Click here to show or hide the answer key

15 km

Solution

Click here to show or hide the solution

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

Tags:

Motion Problem

First Half of the Distance

Return Trip

Add new comment
6492 reads

More Reviewers

Algebra	Engineering Mechanics
Spherical Trigonometry	Strength of Materials
Plane Trigonometry	Structural Analysis
Plane Geometry	General Engineering
Solid Geometry	Derivation of Formulas
Analytic Geometry	Fluid Mechanics and Hydraulics
Integral Calculus	Geotechnical Engineering
Differential Calculus	Reinforced Concrete Design
Elementary Differential Equations	Surveying and Transportation Engineering
Advance Engineering Mathematics	Timber Design
Engineering Economy

07 - A Man Covers an Unknown Distance at Different Rates

More Reviewers

Algebra