1. Tim and Brad are building a racecar. Tim can build the car in months less time than Brad. Together they can do the job in 7 months. How long will it take each of them if they work alone? Give your answer to the nearest tenth.


2. Nick and Rhonda are building a square pond in their backyard. They wish to put a 2 foot wide brick border around the outside. If the total area of the border and pond is 196 square feet, find the dimensions of the pond?

The first problem involves rates and you set it up by setting Tim's and Brad's rates equal to their team rate. Since you didn't specify how much faster Tim works than Brad, I'll assume it is 2 months faster. You can modify it for whatever it is. So the equation to solve is 1/t +1/(t+2) = 1/7 where t equals the time it takes Tim to build a car. This equation simplifies to the quadratic t2 - 12t - 14 = 0 and you have to use the general solution to solve it. Tim takes 13.1 months and Brad 15.1 months.

The second problem sets up as (x+4)(x+4) = 196 and this becomes x2 + 8x - 180 = 0 which has the solutions x = 10 and -18. Only 10 makes sense, so the pond must be 10 ft x 10 ft.