Speed
A man makes a trip by automobile at an average speed of 50 mph. He returns over the same route at an average speed of 45 mph. His average speed for the entire trip is:
47 7/19 mph
The sum of two numbers is 1 and their product is 1. Find the sum of their squares.
-1
Suppose a and b are the roots of x^2 + 7x + 9.
Find the value of a^2 + b^2.
31
I rode my bike 30 miles. If I had increased my average speed by 3 mph, I would have decreased my travel time by 20 minutes. How many miles per hour was my original speed?
15 mph
If 2^{1998}-2^{1997}-2^{1996}+2^{1995} = k* 2^{1995}, what is the value of k?
3
Suppose a and b are the roots of x^2 - 8x +11.
Find the value of a^3 + b^3.
248
Nick is a runner, and his goal is to complete four laps around a circuit at an average speed of 10 mph. If he completes the first three laps at a constant speed of only 9 mph, what speed does he need to maintain in miles per hour on the fourth lap to achieve his goal?
15 mph
Let x+y = 11 and x^2+ y^2 = 325. What is the value of x^3 + y^3?
4697
The product of the roots of the quadratic 6x^2 + cx + 4 is 2 greater than the sum of the roots, and c is a constant.
What is c?
8