Chapter 12.1, Problem 50E

To determine

To calculate: The rate at which he input the data into computer by noon.

Answer to Problem 50E

The rate at which he input the data into computer by noonis $\frac{10}{3}\text{ per minute}$ .

Explanation of Solution

Given information:

For each half hour he works the rate at which data is input is 2 data items faster. The data input rate is 3 data items per minute when he started to work at $9:00\text{ A}\text{.M}.$ .

Formula used:

A sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

The $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ .

Calculation:

Consider the each half hour he works the rate at which data is input is 2 data items faster. The data input rate is 3 data items per minute when he started to work at $9:00\text{ A}\text{.M}.$ .

The above situation forms an arithmetic sequence as discussed below.

Since he input 3 data items per minute so data items entered in first half an hour are,

  $3\cdot 30=90$

So, $a_1=90$ .

Since each half hour he works the rate at which data is input is 2 data items faster.

So, $d=2$ .

Between $9:00\text{ A}\text{.M}.$ and noon there are 6 half hours. So, $n=6$ .

Recall that $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ .

Therefore, number of data inputs till noon is,

  $\begin{array}{c}{a}_6=90+\left(6-1\right)2\\ =90+10\\ =100\end{array}$

So, the rate at which he input the data into computer by noon is,

  $\frac{100}{30}=\frac{10}{3}\text{ per minute}$

Thus, the rate at which he input the data into computer by noon is $\frac{10}{3}\text{ per minute}$ .