# Exercises - Applications

1. Car $X$ travels $20$ miles per hour faster than car $Y$. Car $X$ can travel $100$ miles in the same time it takes car $Y$ to travel $60$ miles. Find the speed of each car.   $\ans{\begin{array}{l}\textrm{car$X: \, 50$mph}\\\textrm{car$Y: \, 30$mph}\end{array}}$

2. A group of students wish to split the $\$100$cost of reserving a room for a party. When$5$more students join the group, the cost per student is reduced by$\$10$. How many students were in the original group? What was the original cost per student?   $\ans{\begin{array}{l}\textrm{number of students:$5$}\\\textrm{cost per student:$\$20$}\end{array}}$3. An open box is made from a$10$inch by$14$inch piece of cardboard by cutting a square from each corner and folding up the edges. If the area of the bottom of the box is$60$square inches, what is the length of the sides of the squares removed?$\ans{2 \textrm{ inches } \times 2 \textrm{ inches}}$4. The speed of a boat in still water is$10$mph. It travels$15$miles upstream and$15$miles downstream in a total time of$4$hours. What is the speed of the current?$\ans{5 \textrm{ mph}}$5. A rectangular garden is$12$feet long and$10$feet wide. Part of the garden is torn up to install a sidewalk of uniform width around the garden. If the area of the new garden is$48$square feet, find the width of the sidewalk.$\ans{2 \textrm{ feet wide}}\$