7. Two automobiles travel toward each other over a distance of 120 miles. A leaves at 9 a.m., 1 hour before B starts to meet him, and they meet at 12:00 m. If each had started at 9:15 a.m., they would have met at 12:00 m. also. Find the rate at which each traveled. (M. I. T.)
Quadratic Equations
1. Telegraph poles are set at equal distances apart. In order to have two less to the mile, it will be necessary to set them 20 feet farther apart. Find how far apart they are now. (Yale.)
2. The distance
that a body falls from rest in t seconds is given by the formula
A man drops a stone into a well and hears the splash after 3 seconds. If the velocity of sound in air is 1086 feet a second, what is the depth of the well? (Yale.)
3. It requires 2000 square tiles of a certain size to pave a hall, or 3125 square tiles whose dimensions are one inch less. Find the area of the hall. How many solutions has the equation of this problem? How many has the problem itself? Explain the apparent discrepancy. (Cornell.)
4. A rectangular tract of land, 800 feet long by 600 feet broad, is divided into four rectangular blocks by two streets of equal width running through it at right angles. Find the width of the streets, if together they cover an area of 77,500 square feet. (M. I. T.)