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63

Jessica and Derick are working together to paint a room. If Jessica paints the room alone, it would take her \(9\) hours to complete the job. If Derick paints the room alone, it would take him \(18\) hours to complete the job. Answer the following question:

If they work together, it would take them hours to complete the job. Use a decimal in your answer if needed.

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64

There are three pipes at a tank. To fill the tank, it would take Pipe A \(4\) hours, Pipe B \(12\) hours, and Pipe C \(3\) hours. Answer the following question:

If all three pipes are turned on, it would take hours to fill the tank.

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65

Neil and Nathan are working together to paint a room. Neil works \(5.5\) times as fast as Nathan does. If they work together, it took them \(11\) hours to complete the job. Answer the following questions:

If Neil paints the room alone, it would take him hours to complete the job.

If Nathan paints the room alone, it would take him hours to complete the job.

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66

Two pipes are being used to fill a tank. Pipe A can fill the tank \(4.5\) times as fast as Pipe B does. When both pipes are turned on, it takes \(9\) hours to fill the tank. Answer the following questions:

If only Pipe A is turned on, it would take hours to fill the tank.

If only Pipe B is turned on, it would take hours to fill the tank.

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67

Aleric and Carmen worked together to paint a room, and it took them \(4\) hours to complete the job. If they work alone, it would take Carmen \(6\) more hours than Aleric to complete the job. Answer the following questions:

If Aleric paints the room alone, it would take him hours to complete the job.

If Carmen paints the room alone, it would take her hours to complete the job.

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68

If both Pipe A and Pipe B are turned on, it would take \(2\) hours to fill a tank. If each pipe is turned on alone, it takes Pipe B \(3\) fewer hours than Pipe A to fill the tank. Answer the following questions:

If only Pipe A is turned on, it would take hours to fill the tank.

If only Pipe B is turned on, it would take hours to fill the tank.

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69

Town A and Town B are \(720\) miles apart. A boat traveled from Town A to Town B, and then back to Town A. Since the river flows from Town B to Town A, the boatâs speed was \(30\) miles per hour faster when it traveled from Town B to Town A. The whole trip took \(20\) hours. Answer the following questions:

The boat traveled from Town A to Town B at the speed of miles per hour.

The boat traveled from Town B back to Town A at the speed of miles per hour.

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70

A river flows at \(13\) miles per hour. A boat traveled with the current from Town A to Town B, which are \(360\) miles apart. Then, the boat turned around, and traveled against the current to reach Town C, which is \(100\) miles away from Town B. The second leg of the trip (Town B to Town C) took the same time as the first leg (Town A to Town B). During this whole trip, the boat was driving at a constant still-water speed. Answer the following question:

During this trip, the boatâs speed on still water was miles.

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71

A river flows at \(8\) miles per hour. A boat traveled with the current from Town A to Town B, which are \(130\) miles apart. The boat stayed overnight at Town B. The next day, the waterâs current stopped, and boat traveled on still water to reach Town C, which is \(200\) miles away from Town B. The second leg of the trip (Town B to Town C) took \(5\) hours longer than the first leg (Town A to Town B). During this whole trip, the boat was driving at a constant still-water speed. Find this speed.

Note that you should not consider the unreasonable answer.

During this trip, the boatâs speed on still water was miles per hour.

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72

Town A and Town B are \(600\) miles apart. With a constant still-water speed, a boat traveled from Town A to Town B, and then back to Town A. During this whole trip, the river flew from Town A to Town B at \(11\) miles per hour. The whole trip took \(10\) hours. Answer the following question:

During this trip, the boatâs speed on still water was miles per hour.

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73

Town A and Town B are \(200\) miles apart. With a constant still-water speed of \(45\) miles per hour, a boat traveled from Town A to Town B, and then back to Town A. During this whole trip, the river flew from Town B to Town A at a constant speed. The whole trip took \(9\) hours. Answer the following question:

During this trip, the riverâs speed was miles per hour.

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74

Suppose that a large pump can empty a swimming pool in \(33\ {\rm hr}\) and that a small pump can empty the same pool in \(49\ {\rm hr}\text{.}\) If both pumps are used at the same time, how long will it take to empty the pool?

If both pumps are used at the same time, it will take to empty the pool.

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75

The winner of a \(6\ {\rm mi}\) race finishes \(15.05\ {\rm min}\) ahead of the second-place runner. On average, the winner ran \(0.6\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\) faster than the second place runner. Find the average running speed for each runner.

The winner's average speed was and the second-place runner's average speed was .

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76

In still water a tugboat can travel \(20\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\text{.}\) It travels \(43\ {\rm mi}\) upstream and then \(43\ {\rm mi}\) downstream in a total time of \(4.35\ {\rm hr}\text{.}\) Find the speed of the current.

The current's speed is .

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77

Without any wind an airplane flies at \(246\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\text{.}\) The plane travels \(620\ {\rm mi}\) into the wind and then returns with the wind in a total time of \(5.07\ {\rm hr}\text{.}\) Find the average speed of the wind.

The wind's speed is .

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78

When there is a \(22.4\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\) wind, an airplane can fly \(800\ {\rm mi}\) with the wind in the same time that it can fly \(642\ {\rm mi}\) against the wind. Find the speed of the plane when there is no wind.

The plane's airspeed is .

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79

It takes one employee \(4.5\ {\rm hr}\) longer to mow a football field than it does a more experienced employee. Together they can mow the grass in \(2.8\ {\rm hr}\text{.}\) How long does it take each person to mow the football field working alone?

The more experienced worker takes to mow the field alone, and the less experienced worker takes .

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80

It takes one painter \(19\ {\rm hr}\) longer to paint a house than it does a more experienced painter. Together they can paint the house in \(25\ {\rm hr}\text{.}\) How long does it take for each painter to paint the house working alone?

The more experienced painter takes to paint the house alone, and the less experienced painter takes .