Convert 90 minutes to hours.
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Solve uniform motion applications
When planning a road trip, it often helps to know how long it will take to reach the destination or how far to travel each day. We would use the distance, rate, and time formula,
which we have already seen.
In this section, we will use this formula in situations that require a little more algebra to solve than the ones we saw earlier. Generally, we will be looking at comparing two scenarios, such as two vehicles travelling at different rates or in opposite directions. When the speed of each vehicle is constant, we call applications like this
uniform motion problems .
Our problem-solving strategies will still apply here, but we will add to the first step. The first step will include drawing a diagram that shows what is happening in the example. Drawing the diagram helps us understand what is happening so that we will write an appropriate equation. Then we will make a table to organize the information, like we did for the money applications.
The steps are listed here for easy reference:
Use a problem-solving strategy in distance, rate, and time applications.
Read the problem. Make sure all the words and ideas are understood.
Draw a diagram to illustrate what it happening.
Create a table to organize the information.
Label the columns rate, time, distance.
List the two scenarios.
Write in the information you know.
Identify what we are looking for.
Name what we are looking for. Choose a variable to represent that quantity.
Complete the chart.
Use variable expressions to represent that quantity in each row.
Multiply the rate times the time to get the distance.
Translate into an equation.
Restate the problem in one sentence with all the important information.
Then, translate the sentence into an equation.
Solve the equation using good algebra techniques.
Check the answer in the problem and make sure it makes sense.
Answer the question with a complete sentence.
An express train and a local train leave Pittsburgh to travel to Washington, D.C. The express train can make the trip in 4 hours and the local train takes 5 hours for the trip. The speed of the express train is 12 miles per hour faster than the speed of the local train. Find the speed of both trains.
Solution
Step 1. Read the problem. Make sure all the words and ideas are understood.
Draw a diagram to illustrate what it happening. Shown below is a sketch of what is happening in the example.
Create a table to organize the information.
Label the columns “Rate,” “Time,” and “Distance.”
List the two scenarios.
Write in the information you know.
Step 2. Identify what we are looking for.
We are asked to find the speed of both trains.
Notice that the distance formula uses the word “rate,” but it is more common to use “speed” when we talk about vehicles in everyday English.
Step 3. Name what we are looking for. Choose a variable to represent that quantity.
Complete the chart
Use variable expressions to represent that quantity in each row.
We are looking for the speed of the trains. Let’s let
r represent the speed of the local train. Since the speed of the express train is 12 mph faster, we represent that as
Fill in the speeds into the chart.
Multiply the rate times the time to get the distance.
Step 4. Translate into an equation.
Restate the problem in one sentence with all the important information.
Then, translate the sentence into an equation.
The equation to model this situation will come from the relation between the distances. Look at the diagram we drew above. How is the distance travelled by the express train related to the distance travelled by the local train?
Since both trains leave from Pittsburgh and travel to Washington, D.C. they travel the same distance. So we write:
Step 5. Solve the equation using good algebra techniques.
Now solve this equation.
So the speed of the local train is 48 mph.
Find the speed of the express train.
The speed of the express train is 60 mph.
Step 6. Check the answer in the problem and make sure it makes sense.
Step 7. Answer the question with a complete sentence.
The speed of the local train is 48 mph and the speed of the express train is 60 mph.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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