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.   $\ans{2 \textrm{ feet wide}}$