Question

Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let P(t), left parenthesis, t, right parenthesis denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula

Answer 1

In 4 hours, Naoya must have read

$\dfrac{55\text{ pages}}{1\text{ h}}\cdot4\text{ h}=220\text{ pages}$

There were 350 pages remaining at the time, so the total number of pages is $220+350=570$.

For each hour of reading, Naoya reads 55 pages, so the number of pages he's finished reading by the $t$'th hour is $55t$. So the number of pages left to read is given by

$P(t)=570-55t$

Answer 2

Answer:

Naoya read 55 pages per hour, so he read 55T pages in T hours.

The total number of pages is comprised of the number of pages Naoya had already read and the number of pages that remained. We can express this with the equation B=55T+R, where:

B represents the book's length

T represents the time (in hours)

R represents the number of remaining pages to read at a given time.

We know that after reading for 44 hours (T=4) Naoya had 330 remaining pages to read (R=330) Let's plug these values into the equation to find the value of B

B=55*4+330=550

Therefore, the book is 550 pages long.

To find how long it took Naoya to finish the entire book, we can plug R=0  into the equation and solve for T.

550 =55T + 0

55T = 550

T= 10

The book is 550 pages long.

It took Naoya 10 hours to read the entire book.

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