Rational Word Problems

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?

•  $\frac{1}{4}+\frac{1}{6}=\frac{1}{t}$  

•  $\frac{1}{4}+\frac{1}{t}=\frac{1}{6}$  

•  $\frac{1}{6}+\frac{1}{t}=\frac{1}{4}$  

•  $t=24$  

Tags

CCSS.HSA.CED.A.1

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?

• $\frac{10}{2-x}=\frac{3}{2+x}$

• $\frac{10}{x-2}=\frac{3}{x+2}$

• $\frac{10}{x+2}=\frac{3}{x-2}$

• $\frac{10}{2+x}=\frac{3}{2-x}$

Tags

CCSS.HSA.CED.A.1

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?

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

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

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

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

Tags

CCSS.HSA.CED.A.1

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?

• $2t+t=3$

• $\frac{1}{3}+\frac{1}{6}=\frac{1}{t}$

• $\frac{1}{t}+\frac{1}{3}=\frac{1}{2t}$

• $\frac{1}{t}+\frac{1}{2t}=\frac{1}{3}$

Tags

CCSS.HSA.CED.A.1

A car travels 400 km in the same time that a freight train travels 300 km. The speed of the car is 25 km/h more than the speed of the train. Find the speed of the car and the speed of the train. (Hint set fractions equal rather than adding to a set time.)

• $\frac{400}{x-25}=\frac{300}{x+25}$

• $\frac{400}{x+25}=\frac{300}{x-25}$

• $\frac{400}{x+25}=\frac{300}{x}$

• $\frac{400}{x}=\frac{300}{x+25}$

Tags

CCSS.HSA.REI.A.2

The time it takes for a canoe to go 4 miles upstream and back 4 miles downstream is 5 hours. The current in the lake is 2 mile per hour.  Find the average speed (rate) of the canoe in still water.

•  $\frac{4}{x+2}+\frac{4}{x-2}=5$  

•  $\frac{4}{2+x}+\frac{4}{2-x}=5$  

•  $\frac{4}{x+2}=\frac{5}{x-2}$  

•  $\frac{4}{2+x}=\frac{5}{2-x}$  

Tags

CCSS.HSA.CED.A.1