WRT Practice PS Set – 2
Work & Rate: Level 2
1.
Machine A can complete a job in 10 hours. Machine B can complete the same job in 15 hours. How long will it take if they work together?
Solution (C):
Rate A = 1/10, Rate B = 1/15.
Combined Rate = \( \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \).
Time = \( \frac{1}{\text{Rate}} = 6 \) hours.
2.
Pipe X fills a tank in 4 hours. Pipe Y fills the same tank in 12 hours. If both pipes are open, how many hours will it take to fill the tank?
Solution (B):
Combined Rate = \( \frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3} \).
Time = 3 hours.
3.
A copy machine makes 40 copies per minute. A second machine makes 60 copies per minute. Working together, how many copies do they make in 5 minutes?
Solution (D):
Combined Rate = \( 40 + 60 = 100 \) copies/minute.
Total = \( 100 \times 5 = 500 \) copies.
4.
If 6 workers can complete a task in 8 days, how many days will it take 4 workers to complete the same task?
Solution (A):
Total Work = \( 6 \times 8 = 48 \) worker-days.
With 4 workers: \( \text{Days} = \frac{48}{4} = 12 \) days.
5.
Alice can type a report in 6 hours. Bob takes 3 hours to type the same report. If they type together, what fraction of the report is done in 1 hour?
Solution (C):
Rate Alice = 1/6. Rate Bob = 1/3.
Combined Rate = \( \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \).
In 1 hour, they complete 1/2 of the report.
6.
Pump A empties a pool in 5 hours. Pump B empties the same pool in 10 hours. How many hours will it take to empty the pool if both pumps work together?
Solution (E):
Rate = \( \frac{1}{5} + \frac{1}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \).
Time = \( \frac{10}{3} \approx 3.33 \) hours.
7.
A printer prints 300 pages in \(x\) minutes. Another prints 300 pages in \(2x\) minutes. Together, they print 300 pages in 10 minutes. What is \(x\)?
Solution (B):
Rates: \( \frac{1}{x} + \frac{1}{2x} = \frac{1}{10} \).
\( \frac{2+1}{2x} = \frac{1}{10} \implies \frac{3}{2x} = \frac{1}{10} \).
\( 2x = 30 \implies x = 15 \).
8.
A crew of 4 people can paint a fence in 3 hours. If one person joins them (working at the same rate), how many hours will it take the 5 people to paint the fence?
Solution (D):
Total Work = \( 4 \times 3 = 12 \) person-hours.
New Time = \( \frac{12}{5} = 2.4 \) hours.
9.
Carl can plant a garden in 4 hours. Together with Dan, they can plant it in 2.4 hours. How long would it take Dan alone?
Solution (A):
\( \frac{1}{4} + \frac{1}{D} = \frac{1}{2.4} \).
\( \frac{1}{D} = \frac{1}{2.4} – \frac{1}{4} = \frac{10}{24} – \frac{6}{24} = \frac{4}{24} = \frac{1}{6} \).
\( D = 6 \) hours.
10.
A pool has two pipes. Pipe A fills it in 6 hours, Pipe B fills it in 8 hours. If both are opened, how long to fill half the pool?
Solution (C):
Combined Rate = \( \frac{1}{6} + \frac{1}{8} = \frac{4}{24} + \frac{3}{24} = \frac{7}{24} \).
Time for full pool = \( 24/7 \).
Time for half pool = \( \frac{1}{2} \times \frac{24}{7} = \frac{12}{7} \) hours.
Score: 0 / 0