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txayrion
10.10.2019 •
Mathematics
At a lical train station 3 trains are scheduled to leave the station every 48 minutes.
1) write a constant of proportionality equation for this relationship.
2) given the relationship is the same, how many minute have passed after 10 trains have left the station?
3) given the relationship is the same, how many trains have left the station after 8 hours?
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Ответ:
Part 1)![k=\frac{1}{16}\ \frac{trains}{min}](/tpl/images/0305/4633/c07d7.png)
Part 2)![160\ min](/tpl/images/0305/4633/9ec4d.png)
Part 3)![30\ trains](/tpl/images/0305/4633/545d5.png)
Step-by-step explanation:
Part 1) Write a constant of proportionality equation for this relationship
Let
y ----> the number of trains
x ----> the time minutes
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](/tpl/images/0305/4633/7f524.png)
In this problem we have
For x=48 min, y=3 trains
Simplify
The units of the constant of proportionality are![\frac{trains}{min}](/tpl/images/0305/4633/76dee.png)
so
The linear equation is
Part 2) Given the relationship is the same, how many minute have passed after 10 trains have left the station?
For y=10 trains
substitute the value of y in the equation and solve for x
Part 3) Given the relationship is the same, how many trains have left the station after 8 hours?
For x=8 hours
substitute the value of x in the equation and solve for y
But first convert hours to minutes
remember that
substitute
Ответ:
the answer is 7x + 3< 26