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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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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 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 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
= . (1)
What is in the right side ?
- But of course, it is 15 minutes, that are 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 = kilometers.
Thus you found the distance and answered the question.
Answer. The distance from the house to the school is kilometers, or 750 meters.
Now, let us check the solution.
The time from the house to the school = = hours.
The time back, from the school to the house (jogging !) is = of an hours.
The difference is = = of an hour.
Exactly as the condition states.
Now take my congratulations !! You successfully solved the problem.
In this site, there are a lot of lessons on Travel an Distance:
- Travel and Distance problems
- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Using fractions to solve Travel problems
- Unpowered raft floating downstream along a river
- Had a car move faster it would arrive quicker
- How far do you live from school?
- One unusual Travel problem
- Another unusual Travel problem (Arnold's problem on two walking old women)
- Clock problems
- Problems on bodies moving on a circle
- Calculating an average speed: a train going from A to B and back
- One more problem on calculating an average speed
- Travel problem on a messenger moving back and forth along the marching army's column
- A person walking along the street and buses traveling in the same and opposite directions
- A train passing a telegraph post and passing a bridge
- A train passing a platform
- A train passing through a tunnel
- A light-rail train passing a walking person
- A train passing another train
- A man crossing a bridge and a train coming from behind
- Selected Travel and Distance problems from the archive
- Selected problems from the archive on the boat floating Upstream and Downstream
- Selected problems from the archive on a plane flying with and against the wind
- The distance covered by a free falling body during last second of the fall
- OVERVIEW of lessons on Travel and Distance.
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
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".