Chapter 30 · Miscellaneous Problems
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
From Problems from Astronomy and Geometry, exercise 25
The distance of the earth from the sun is 387\frac12 times the earth's distance from the moon. Light traveling 186{,}000 miles per second would require 8 minutes 18\frac{22}{31} seconds longer to go from the earth to the sun than from the earth to the moon. Find each distance.
From Clock and Planet Problems, exercise 2
Miscellaneous problems:
At what time between 7 and 8 o'clock are the hands of a clock together?
From Clock and Planet Problems, exercise 7
Miscellaneous problems:
Venus was in (superior) conjunction April 28, 1909. If Venus revolves about the sun once in 225 days, find the number of days to the next conjunction, and so its approximate date.
From Problems from Astronomy and Geometry, exercise 28
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.
From Common Multiples of Fractions, exercise 15
The method of finding the L.C.M. of two or more fractions or mixed numbers is hinted at in Exercise 14. State a rule therefor. Find by the rule the L.C.M. of 1\frac16, 2\frac13, and 3\frac19.
From Mixture Problems, exercise 22
A chemist has the same acid in two strengths. Eight liters of one mixed with 12 liters of the other gives a mixture 84\% pure, and 3 liters of the first mixed with 2 liters of the second gives a mixture 86\% pure. Find the per cent of purity of each acid.
From Problems from Astronomy and Geometry, exercise 26
The mean distance between Mars and the earth when they are on opposite sides of the sun is 234{,}500{,}000 miles. When the two planets are nearest each other on the same side of the sun, the mean distance between them is 48{,}500{,}000 miles. Find the distance of each from the sun.
From Mixture Problems, exercise 17
How many ounces of alloy must be added to 56 ounces of silver to make a composition 70\% silver?
From Problems from Astronomy and Geometry, exercise 32
A rectangular box is 8 inches long. Its volume is 192 cubic inches and the area of its six faces is 208 square inches. Find the other two dimensions.
From Mixture Problems, exercise 19
A 30-gallon mixture of milk and water tests 16\% cream. How much water has been added if the milk is known to test 20\% cream?
Try y = 2x - 3, x + 2y = 8, x = 3, x^2 + y^2 = 25, or a point (4, 2). Drag to move, scroll to zoom.