Problems

Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1:30$ , traveling due north at a steady $8$ miles per hour. Betsy leaves on her bicycle from the same point at $2:30$ , traveling due east at a steady $12$ miles per hour. At what time will they be exactly the same distance from their …

The instructions on a $350$ -gram bag of coffee beans say that proper brewing of a large mug of pour-over coffee requires $20$ grams of coffee beans. What is the greatest number of properly brewed large mugs of coffee that can be made from the coffee beans in that bag?

What is the value of $9901\cdot101-99\cdot10101?$

In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the right. How many people are in the line?

Cities $A$ and $B$ are $45$ miles apart. Alicia lives in $A$ and Beth lives in $B$ . Alicia bikes towards $B$ at $18$ miles per hour. Leaving at the same time, Beth bikes toward $A$ at $12$ miles per hour. How many miles from City $A$ will they be when they meet?

Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only $\frac{1}{3}$ full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four …

What is the value of $$3+\frac{1}{3+\frac{1}{3+\frac13}}?$$

Define $x\diamond y$ to be $|x-y|$ for all real numbers $x$ and $y.$ What is the value of $$(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?$$

What is the value of $$(2^2-2)-(3^2-3)+(4^2-4)?$$

How many integer values of $x$ satisfy $|x| < 3\pi$ ?

What is the value of $\frac{(2112-2021)^2}{169}$ ?

What is the value of $1234+2341+3412+4123?$

What value of $x$ satisfies $$x- \frac{3}{4} = \frac{5}{12} - \frac{1}{3}?$$

What is the value of $$1 - (-2) - 3 - (-4) - 5 - (-6)?$$

What is the value of $$2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?$$

Alicia had two containers. The first was $\tfrac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\tfrac{3}{4}$ full of water. What is the ratio of the volume of the first container to the volume of the …

What is the value of $$\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?$$

Kate bakes a $20$ -inch by $18$ -inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain?

What is the value of $(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)$ ?

Mary thought of a positive two-digit number. She multiplied it by $3$ and added $11$ . Then she switched the digits of the result, obtaining a number between $71$ and $75$ , inclusive. What was Mary's number?

What is the value of $\dfrac{11!-10!}{9!}$ ?

What is the value of $\frac{2a^{-1}+\frac{a^{-1}}{2}}{a}$ when $a= \tfrac{1}{2}$ ?

What is the value of $(2^0-1+5^2+0)^{-1}\times5?$

What is the value of $2-(-2)^{-2}$ ?

What is $10 \cdot \left(\tfrac{1}{2} + \tfrac{1}{5} + \tfrac{1}{10}\right)^{-1}?$