Rational Applications

A boat goes 10 miles downstream in the same time it can go 3 miles upstream. The speed of the current is 2 miles per hour. Which equation could you use to find the speed of the boat in still water?

• $\frac{10}{2-x}=\frac{3}{2+x}$

• $\frac{10}{x-2}=\frac{3}{x+2}$

• $\frac{10}{x+2}=\frac{3}{x-2}$

• $\frac{10}{2+x}=\frac{3}{2-x}$

Jose left on a vacation and drove towards Ohio at an average speed of 40km/h. Rob left some time later driving in the same direction at an average speed of 48km/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?

• 5 hours
• 6 hours
• 8 hours
• 2 hours

A plane flies 1225 miles with a tailwind in the same time it can go 1100 miles against the wind. The speed of the plane in still air is 575 miles per hour. Which equation would you use to find the speed of the wind?

• $\frac{1225}{575-x}=\frac{1100}{575+x}$

• $\frac{1225}{575+x}=\frac{1100}{575-x}$

• $\frac{1225}{x+575}=\frac{1100}{x-575}$

• $\frac{1225}{x-575}=\frac{1100}{x+575}$

Keith and Melanie were able to reupholster furniture in three hours together. It takes Melanie five hours to do this job alone. Without help, how long would it take Keith to do this job ?

• 5.5

• 6.5

• 7.5

• 8.5

Solve and check for extraneous solutions

• x=5
• x= -5
• No Solution

Which of the following is true - select all that apply - if you know that I can dig a hole in 4 days and my friend Steve can dig it in 5 days.

• I have the quicker rate.

• Steve has the quicker rate.

• If we work together to complete the job, the equation will equal 1.

• This is a subtraction problem.

Bob and Mike are painting walls. Bob can paint 1 wall in 2 hours. When Mike and Bob work together they can paint 2 walls in 3 hrs. How many hours does it take Mike to point 1 wall?

• 7 hours
• 3 hours
• 2 hours
• 6 hours

Katherine can paint a room in 4 hours. Joe needs 6 hours to paint the same room. Which equation would you use to determine how long it takes them to paint the room if they work together?

Solve the equation for x.

• 7
• 6
• 14
• 0

George can build a laptop twice as fast as Kurt. Working together, it takes them 3 hours. Which equation would you use to determine how long it will take Kurt working alone?