Question

I need an expression for this scenario:
Joe and Louise are making a drive from San Diego to Salt Lake City. After four hours of driving they are 507 miles from Salt Lake City. Eight hours into their trip they are only 267 miles away from their destination. Assume they averaged the same speed for the entire trip.

Answer 1

Assume the distance between San Diego and Salt Lake City to be "d" miles.
Assume "s" is the speed in miles per hour.

If "s" is the speed, how many miles will they have traveled in 4 hours?

Answer 2

I can not find the right expression.

Answer 3

Definition of speed is distance / time.
If "s" is the speed, how many miles will they have traveled in 4 hours?
s = distance / time. Therefore, distance = speed * time = s * 4 = 4s

We assumed "d" to be the distance between the two cities.
In 4 hours they have traveled 4s miles from San Diego.
Therefore, the distance to Salt Lake City is: d - 4s which is given as 507
d - 4s = 507 ----- (equation 1).

Use the same method to find another equation after 8 hours of travel.

Answer 4

This is part of the equation:
To find y=-60x+b, you can substitute in one of the coordinate pairs for X and Y. For example you can substitute 4 for X and 507 for Y. this gives 507=(-60)(4)+b. Solve the equation for b, and substitute that value into the expression.

Answer 5

There are many ways of solving this problem. Earlier I showed one way. Above you have a second way to solve the same problem and get the exact same answer. But you will have to explain how you got -60? (not for me but to your instructor).

Answer 6

It showed itself in a hint on the homework site.

Answer 7

What is the question that is asked. Does it say "write the expression for this scenario" ?

Answer 8

We can solve for the speed of travel.
We can solve for the distance between the two cities.
So what is being asked?

Answer 9

It asked for the distance they are from Salt Lake City in miles as an expression.

Answer 10

Okay. Assume y is the distance between their location and Salt Lake City and x is the time they have traveled.
Since the speed is constant, the graph of y vs x will be a straight line.
Therefore, y = mx + b
When x = 4, y = 507. 507 = m(4) + b. 4m + b = 507 ---- (1)
When x = 8, y = 267. 267 = m(8) + b. 8m + b = 267 ---- (2)
You have 2 equations and 2 unknowns, namely, m and b.
Solve for m and b and you will have have an equation connecting distance between them and Salt Lake City ("y") as a function of time ("x").

Answer 11

To get rid of "b", just subtract (2) from (1). Solve for m.

Answer 12

Thank you.

Answer 13

You are welcome. Once you solve for m and b, put that in y = mx + b and the right hand side is the expression they are asking for.