pls solve each problem by using function f(x)=mx+b:?

Question

1. Alina read 56 pages in 3 hours.At the same rate, find the number of hours it will take her to read the remaining 140 pages.
pls with complete solution........

Answer 1

Solve as a proportional problem

3 / 56 = x / 140

The means are 56x

The extremes are 3(140)

56x = 3(140)

The distributive property on the right side of the equation

56x = 420

Divide both sides of the equation by 56

56x / 56 = 420 / 56

x = 420 / 56

x = 7.5 hours

It will take Alina 7.5 hours to read the remaining 140 pages.

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Answer 2

Assuming a linear relationship...

If 56 pages are read in 3 hours, this means 56/3 would be the number of pages she can read in one hour.

Therefore, our function is f(x) = (56/3)x, where the slope (m) = 56/3.

We need to set the function equal to 140 pages and then solve for x as follows...

(56/3)x = 140

Step 1: Multiply both sides of the equation by 3...

56x = 140*3
56x = 420

Step 2: Divide both sides of the equation by 56...

56x / 56 = 420/56
x = 7.5

Therefore, it will take her 7.5 hours to read the remaining pages.

Answer 3

F(x) = Mx + B
F(3) = 56
3M + B = 56

Setting B = 0, M = 56/3

F(x) = (56/3)x

We want to find x where F(x) = 140. So,

140 = (56/3)x
(56/3)x = 140
x = (3*140)/56
x = 7.5

7.5 hours.

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Now, a simpler way to solve this would have been to say:

It will take her (140/(56/3)) = 7.5 hours. No F(x)=Mx+B stuff needed.

Answer 4

Alina reads 56pages in 3hrs,
rate of reading=56p/3hrs=56/3page/hr,
therefore 140 pages will be in 140*56/3
=(140*56)/3=7.5hrs
OR
f(x)=mx+b
f(3)=3m+b=56....b=0
therefore, m=56/3
now f(x)=(56/3)x=140 x=(140*3)/56=7.5hrs