Question 1063893
.
Dahlia walks from her house at 2 km/h. After school, she jogs back home at 6 km/h and saves 15 min. How far does Dahlia live from school?
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<pre>
Let D be the distance from the house to the school, in kilometers.

You understand, even without my explanations, that the returning way has the same length. 

OK, very good !

The time Dahlia spent walking from her house to the school, is {{{D/2}}} hours.
    ( I simply divided the distance by the speed to get the time. Did I do it correct ? Do you agree ?)


The time Dahlia spent walking the school to his house, is {{{D/6}}} hours.
    ( Again, I simply divided the distance by the speed to get the time. Did I do it correct ?  Do you agree ?)


Now, she jogs back in 15 minutes sooner, as the condition says. Agree ?

It means that 

{{{D/2 - D/6}}} = {{{1/4}}}.     (1)

What is {{{1/4}}} in the right side ?

- But of course, it is 15 minutes, that are {{{1/4}}} of an hour.


Great !!  Now you have this equation for "D", which serves for you to solve it and find "D".


How to solve it ?  - Very good question !


Simply multiply both sides of (1) by the common denominator, which is 12. You will get

6D - 2D = 3,   or

4D = 3.

Hence, D = {{{3/4}}} kilometers.

Thus you found the distance and answered the question.

<U>Answer</U>. The distance from the house to the school is {{{3/4}}} kilometers, or 750 meters.


Now, let us check the solution.


The time from the house to the school = {{{((3/4))/2}}} = {{{3/8}}} hours.

The time back, from the school to the house (jogging !) is {{{((3/4))/6}}} = {{{1/8}}} of an hours.

The difference is {{{3/8 - 1/8}}} = {{{2/8}}} = {{{1/4}}} of an hour.
Exactly as the condition states.
</pre>

Now take my congratulations !!  You successfully solved the problem.


In this site, there are a lot of lessons on Travel an Distance: 

&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=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> 

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Had-a-car-move-faster-it-would-arrive-quicker.lesson>Had a car move faster it would arrive quicker</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/How-far-do-you-live-from-school.lesson>How far do you live from school?</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/One-unusual-Travel-problem.lesson>One unusual Travel problem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Another-unusual-Travel-problem.lesson>Another unusual Travel problem (Arnold's problem on two walking old women)</A> 

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Problems-on-bodies-moving-on-a-circle.lesson>Problems on bodies moving on a circle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Calculating-an-average-speed.lesson>Calculating an average speed: a train going from A to B and back</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/One-more-problem-on-calculating-an-average-speed.lesson>One more problem on calculating an average speed</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-problem-on-a-messenger-moving-back-and-forth-along-the-marching-army-column.lesson>Travel problem on a messenger moving back and forth along the marching army's column</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/A-person-walking-along-the-street-and-the-buses-traveling-in-the-same-and-opposite-directions.lesson>A person walking along the street and buses traveling in the same and opposite directions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-telegraph-post-and-passing-a-bridge.lesson>A train passing a telegraph post and passing a bridge</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-platform.lesson>A train passing a platform</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-a-tunnel.lesson>A train passing through a tunnel</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-light-rail-train-passing-a-walking-person.lesson>A light-rail train passing a walking person</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/A-train-passing-another-train.lesson>A train passing another train</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/A-man-crossing-a-bridge-when-a-train-comes-from-behind.lesson>A man crossing a bridge and a train coming from behind</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-Travel-and-Distance-problems-from-the-archive.lesson>Selected Travel and Distance problems from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-plane-flying-with-and-against-the-wind.lesson>Selected problems from the archive on a plane flying with and against the wind</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/The-distance-covered-by-a-free-falling-body-during-last-second-of-the-fall.lesson>The distance covered by a free falling body during last second of the fall</A> 

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


Too much ??  Then choose any of them which seems to be most interesting to you.


Happy learning !!



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the section "<U>Word problems</U>", the topic "<U>Travel and Distance problems</U>".