Arithmetic Reasoning - Fraction (Extended)

In classical algebraic rate problems, which equation correctly establishes the relationship between the total work completed (W), the rate of work (R), and the time spent working (T)?

W = R x T (Work equals rate multiplied by time)

What term defines the specific fraction or amount of a single job completed by a worker or system in one unit of time?

Unit Work Rate

When two or more workers or machines operate simultaneously and independently on the exact same task, how is their collective output per unit time determined?

Their individual unit work rates are added together to determine their combined rate.

If Worker A can complete a task twice as fast as Worker B, which mathematical expression correctly reflects Worker A's rate (Ra) relative to Worker B's rate (Rb)?

Ra = 2Rb (Worker A's rate is double Worker B's rate)

Sarah can paint a wall in 6 hours. If she works together with her assistant who paints three times as fast as she does, how long will it take them to finish painting the wall together?

1.5 hours

Machine A takes 10 hours to fill a container, while Machine B takes 15 hours to fill the same container. If both machines are operated simultaneously, how many hours will it take to fill the container?

6 hours

An inlet pipe can fill a water tank in 4 hours, while a drain pipe can completely empty the full tank in 12 hours. If both the inlet pipe and the drain pipe are left open at the same time, how long will it take to fill an empty tank?

6 hours

Worker X can complete a job in 12 hours. Worker Y can complete the same job in 6 hours. Worker X starts the job alone and works for 3 hours before Worker Y joins in. How many additional hours will it take for both workers to finish the remainder of the job together?

3.0 hours

Carlos can paint a room in 8 hours. Working together with his brother, who paints twice as fast as Carlos, how long will it take them to finish painting the room together?

2.67 hours

Maya can paint a fence in 3 & 1/3 hours (10/3 hours). If she works with a partner who paints at half her speed, how long will it take them to paint the fence together?

2.22 hours

Printer A takes 12 minutes to print a batch of reports. Printer B takes 24 minutes to print the exact same batch. If both printers are used simultaneously, how many minutes will it take to complete the print job?

8 minutes

Three automated assembly lines work together to package an order. Line 1 completes the job in 4 hours alone, Line 2 completes it in 6 hours alone, and Line 3 completes it in 12 hours alone. How long will it take all three lines working together to finish the order?

2 hours

Pipe A can fill a pool in 5 hours. Pipe B can fill the same pool in 10 hours. However, a drain pipe at the bottom can empty the full pool in 20 hours. If all three pipes are opened at once, how long will it take to fill the pool?

4.0 hours

An inflow pipe can fill a chemical reactor in 6 hours. Due to a leakage valve at the bottom, it takes 9 hours to fill the reactor when the leak is active. How long would it take the leak alone to empty a fully filled reactor?

18 hours

Painter A can finish a job in 10 hours, while Painter B can finish it in 15 hours. Painter A works alone for 4 hours and then leaves. Painter B takes over to complete the remaining work alone. How many total hours did Painter B spend working?

9 hours

Alice can complete a design project in 12 days, and Bob can complete it in 24 days. Alice starts working alone for 3 days. Then Bob joins her, and they work together until the project is finished. What is the total number of days taken from start to finish to complete the project?

9 days