Lesson Using fractions to solve Travel problems

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<H2>Using fractions to solve Travel problems</H2>

In this lesson some typical &nbsp;<U>Travel problems</U>&nbsp; are presented that are very similar to the problems on &nbsp;<U>Joint work</U>. &nbsp;You will learn how to solve such problems using fractions.

<H3>Problem 1</H3>The car covers the distance between two cities in &nbsp;20&nbsp; hours. &nbsp;The truck can cover this distance in &nbsp;30&nbsp; hours. 
The car and the truck started moving simultaneously from these cities toward each other. 
When will the car and the truck get passing each other?

<B>Solution</B>

The car covers &nbsp;{{{1/20}}}&nbsp; of the whole distance in one hour.

The truck covers &nbsp;{{{1/30}}}&nbsp; of the whole distance in one hour.

Since the car and the truck are moving toward each other, &nbsp;the distance between the car and the truck is decreased each hour by

{{{1/20}}} + {{{1/30}}} = {{{3/60}}} + {{{2/60}}} = {{{5/60}}} = {{{1/12}}}

of its original value which is equal to the distance between the cities.

Hence, &nbsp;it will take &nbsp;12&nbsp; hours for the car and the truck to get passing each other.

<B>Answer</B>. The car and the truck will get passing each other in &nbsp;12&nbsp; hours.

<H3>Problem 2</H3>The car covers the distance between two cities in &nbsp;4&nbsp; hours. &nbsp;The truck can cover this distance in &nbsp;6&nbsp; hours. 
The car and the truck started moving simultaneously from these cities in one direction in a way that the car follows the truck.
When will the car catch up with the truck?

<B>Solution</B>

The car covers &nbsp;{{{1/4}}}&nbsp; of the distance between the cities in one hour.

The truck covers &nbsp;{{{1/6}}}&nbsp; of the same distance in one hour.

Since the car and the truck are moving in one direction, &nbsp;the distance between the car and the truck is decreased each hour in

{{{1/4}}} - {{{1/6}}} = {{{3/12}}} - {{{2/12}}} = {{{1/12}}}

of its original value which is equal to the distance between the cities.

Hence, &nbsp;the car will catch up with the truck in &nbsp;12&nbsp; hours.

<B>Answer</B>. The car will catch up with the truck in &nbsp;12&nbsp; hours.

My other introductory lessons on &nbsp;<B>Travel and Distance</B>&nbsp; problems in this site are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems-for-two-bodies-moving-toward-each-other.lesson>Travel and Distance problems for two bodies moving in opposite directions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-catching-up-Travel-and-Distance-problems.lesson>Travel and Distance problems for two bodies moving in the same direction (catching up)</A>

My other lessons on fractions in this site are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-word-problems.lesson>Using fractions to solve word problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Calculations-with-fractions.lesson>Calculations with fractions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Advanced-problems-on-ratios.lesson>Advanced problems on ratios</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertainment-problem-on-fractions.lesson>Entertainment problems on fractions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/NumericFractions/OVERVIEW-of-my-lessons-on-fractions.lesson>OVERVIEW of my lessons on fractions</A>