How would I write the equation?

Question

Can anyone help me plzz,Well I have this problem:Construction began several months ago,and approximately 87 miles of highway have been completed.The total length of the highway will be 267 miles.You estimate that new consturction can proceed at the rate of one fifth mile per day. Write an equation that represents the number of completed miles in terms of the number of days?So I'm really confused on how to write it...Help me plzzz...

Answer 1

87=1/5*x=total number of completed miles where x=# of days

87 is already completed so u add that to the total
1/5 is u get that much done in a day so however many days u have u multiply by 1/5 and add it onto 87 to get the total amount of miles. of course, the 267 is the ending number, meaning, u can't go over that since thats how long the high way is going to be

Answer 2

Well, for every day 1/5 of a mile of highway can be completed. so let's call y the number of miles, x the number of days.
On the 0th day, 87 miles have already been completed. so the y intercept has to be 87. So, we get the following:

y=1/5x+87

However, construction doesn't go on forever. Once we reach 267 miles we stop. We will reach 267 on what day?
267=1/5x+87
x=900

So for x>900, y = 267 because we're not making anymore road after that. So, we get the answer:

y=1/5x+87, for x<=900
y=267, for x>900

This kind of function, which is defined by different equations depending on the value of x, is called a piecewise equation, in case you were wondering.

Answer 3

I've thought of a couple of different ways to intemperate this problem.

1) Maybe the problem is asking "how many days will it take to finish the highway. I would write that in one of the following ways:

(267-87)/0.2

"The quotient of the difference of the number of anticipated miles minus the number of miles completed, divided by the number of miles per day".

Or with variables, consider T = number of anticipated miles, C = number of miles completed, and P = number of miles per day. Write this as "(t-c)/p"

This would conclude that it will probably take 900 more days to complete the 267 miles.


2) The problem might also be asking "how long did it take to complete the 87 miles?" I would write that in one of these ways:

87/0.2

"The quotient of the number of completed miles divided by the number of miles per day."

Or with variables: Consider C = number of miles completed and P = number of miles per day. Write the expression as "C/P"

This would conclude that it probably took 435 days to complete the 87 miles.

Answer 4

the number of the completed miles
y= 87+(267-87)*(1/5)* x

Answer 5

CompletedMiles = 87 + 1/5*days

Answer 6

87 + 1/5 d = 267

Answer 7

That is easy...

We know that we have already completed 87 miles, so we will always add 87 to the number of miles.

Here we go:
no. of completed miles after 1 day: 87 + 1/5
no. of completed miles after 2 days: 87 + 2/5
no. of completed miles after 3 days: 87 + 3/5
no. of completed miles after 4 days: 87 + 4/5
no. of completed miles after x days: 87 + x/5

If we let d = the number of days of construction and
M = number of miles of highway completed, then

M = 87 + d/5

^_^

Answer 8

X=87x5
X is the number of days it took to complete the first 87 miles.

Answer 9

L = t/5 + 87

t is the time in days and L is the length in miles.

Answer 10

1/5 is 0.2 if you are using calculator to calculate.