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._) 5. (_a_) The height y to which a ball thrown vertically upward with a velocity of 100 feet per second rises in x seconds is given by the formula, y = 100x - 16x^2. In how many seconds will the ball rise to a height of 144 feet? (_b_) Draw the graph of the equation y = 100x - 16x^2. (_College Entrance Board._) 6. Two launches race over a course of 12 miles. The first steams 7-1/2 miles an hour. The other has a start of 10 minutes, runs over the first half of the course with a certain speed, but increases its speed over the second half of the course by 2 miles per hour, winning the race by a minute. What is the speed of the second launch? Explain the meaning of the negative answer. (_Sheffield Scientific School._) 7. The circumference of a rear wheel of a certain wagon is 3 feet more than the circumference of a front wheel. The rear wheel performs 100 fewer revolutions than the front wheel in traveling a distance of 6000 feet. How large are the wheels? (_Harvard._) 8. A man starts from home to catch a train, walking at the rate of 1 yard in 1 second, and arrives 2 minutes late. If he had walked at the rate of 4 yards in 3 seconds, he would have arrived 2-1/2 minutes early. Find the distance from his home to the station. (_College Entrance Board._) ~Simultaneous Quadratics~ 1. Two cubical coal bins together hold 280 cubic feet of coal, and the sum of their lengths is 10 feet. Find the length of each bin. 2. The sum of the radii of two circles is 25 inches, and the difference of their areas is 125[pi] square inches. Find the radii. 3. The area of a right triangle is 150 square feet, and its hypotenuse is 25 feet. Find the arms of the triangle. 4. The combined capacity of two cubical tanks is 637 cubic feet, and the sum of an edge of one and an edge of the other is 13 feet. (_a_) Find the length of a diagonal of any face of each cube. (_b_) Find the distance from upper left-hand corner to lower right-hand corner in either cube. 5. A and B run a mile. In the first heat A gives B a start of 20 yards and beats him by 30 seconds. In the second heat A gives B a start of 32 seconds and beats him by 9-5/11 yards. Find the rate at which each runs. (_Sheffield._)