Math problem involving reciprocal of linear functions

In summary, the conversation discusses how to solve for time in an equation involving distance and speed. The equation is t = distance / speed, and the answer is confirmed by plugging in the given values. The conversation also discusses the relationship between time and speed, where as one increases, the other decreases and vice versa.
  • #1
Matt1234
142
0

Homework Statement



http://img97.imageshack.us/img97/1521/lastscano.jpg

Homework Equations



avg speed = distance / time


The Attempt at a Solution



not sure how to go about this one, looking for a few hints on how to get the equation.

answer is :
t = 3850 /v

But I am not sure why.

thank you
 
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  • #2
Matt1234 said:

Homework Statement



http://img97.imageshack.us/img97/1521/lastscano.jpg

Homework Equations



avg speed = distance / time
You show the equation above as being relevant, but I'm not sure that you are really convinced. Can you solve this equation for time in terms of the other two variables.
Matt1234 said:

The Attempt at a Solution



not sure how to go about this one, looking for a few hints on how to get the equation.

answer is :
t = 3850 /v

But I am not sure why.

thank you
I'm not sure why either. There's either a typo in your answer sheet or you wrote it incorrectly.
 
Last edited by a moderator:
  • #3
just confirmed the answer it is as i typed it.
 
  • #4
t = distance / v

distance = t * v
distance = 11 * 350
distance = 3850

We know distance is 3850km since it takes 11 hours to reach from Quebec City to Montreal at a speed of 350km/h. Time is also inversely proportional to speed so that means as time goes up, speed goes down and vice-versa.

t = 3850/v

To conform this is correct, we will plug the original speed into the equation.
t = 3850/350
t = 11h

If time was lower than 11 (we'll use 5h), speed should go up.
t = 3850/v
5 = 3850/v
v = 3850/5
v = 770 km/h

If time was higher, speed should go down. So let's use 20 hours.
t = 3850/v
20 = 3850/v
v = 192.5 km/h
 
  • #5
thank you very much, that helped alot. Pretty easy i just didnt see it. :)
 
  • #6
Anytime! Good luck. :)
 

Related to Math problem involving reciprocal of linear functions

What is a reciprocal of a linear function?

A reciprocal of a linear function is the inverse of the function, meaning that the output becomes the input and vice versa. It can also be represented as 1 divided by the linear function.

How do you find the reciprocal of a linear function?

To find the reciprocal of a linear function, you can flip the coefficients of the function and change the sign of the exponent. For example, the reciprocal of f(x) = 2x + 3 would be 1/(2x + 3) or (2x + 3)^-1.

What is the domain and range of a reciprocal of a linear function?

The domain of a reciprocal of a linear function is all real numbers except for the value that would make the linear function equal to 0. The range is also all real numbers except for 0, since a reciprocal cannot have a value of 0.

How do you graph a reciprocal of a linear function?

To graph a reciprocal of a linear function, first graph the original linear function. Then, plot points that are the reciprocal of the original points. Connect these points to create the graph of the reciprocal function. Keep in mind that the reciprocal function may have vertical and horizontal asymptotes.

What are some real-life applications of reciprocal of linear functions?

Reciprocal of linear functions can be used in physics to model relationships between variables, such as the relationship between force and distance. They can also be used in economics to calculate marginal cost and marginal revenue. In engineering, they are used in circuit analysis to calculate voltage, current, and resistance.

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