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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

Page 150 of 227

Table of Contents

XIII.

The Greenwich clock strikes the hours from $1$ to $24$ . How many times does it strike in $24$ hours?

In a potato race each man picked up $50$ potatoes placed in line a yard apart, and the first potato one yard from the basket, picking up one potato at a time and bringing it to the basket. How many yards did each man run, the start being made from the basket?

A heavy body falling from a height falls $16.1$ feet the first second, and in each succeeding second $32.2$ feet more than in the second next preceding. How far will a body fall in $19$ seconds?

A stone dropped from a bridge reached the water in just $3$ seconds. Find the height of the bridge. (See Ex. 11.)

The arithmetical mean between two numbers is $13$ , and the mean between the double of the first and the triple of the second is $33 \frac{1}{2}$ . Find the numbers.

Find three numbers of an arithmetical series whose sum shall be $27$ , and the sum of the first and second shall be $f r a c 45$ of the sum of the second and third.

A travels uniformly $20$ miles a day; B travels $8$ miles the first day, $12$ the second, and so on, in arithmetical progression. If they start Monday morning from the same place and travel in the same direction, how far apart will they be Saturday night?

The sum of three terms of an arithmetical progression is $36$ , and the square of the mean exceeds the product of the other two terms by $49$ . Find the numbers.

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