August 2019

Car A drives East at 20 kph at half an hour earlier than car B that started at the same point at 50 kph. How long will car B overtake car A, in minutes?

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?

Solve for C from
$$\dfrac{6x^2 + x - 37}{(x - 3)(x + 2)(x - 1)} = \dfrac{A}{x - 3} + \dfrac{B}{x + 2} + \dfrac{C}{x - 1}$$

Find d so that x + 6 is a factor of x⁴ + 4x³ - 21x² + dx + 108.

A student in a chemistry laboratory wants to form a 32-milliliter mixture of two solutions to contain 30% acid. Solution A contains 42% acid and solution B contains 18% acid. How many milliliters of each solution must be used?

If 1/4 of a mixture of rice and corn was replaced by corn alone, the resulting mixture becomes 55% corn. What was the percentage of corn in the original mixture?

Three boys and two girls are to be picked from a class of 15 in which 9 are girls. How many ways can this be done?