r × t = w
16 t =^12Solve for t: t =1
2
1
6=^12 × 6 = 3.
- B Let r be the rate of each machine. If 4 work together, their combined rate
is 4r. You are told that these 4 machines will fill the production lot in 3 hours.
Plug these values into the r × t = w formula:
r × t = w
↓
4 r × 3 = 1
12 r = 1
r = 121
The rate of each machine, in production lots/hour, is 121. Now plug this value
into the r × t = w formula to determine how many machines, y, would be
necessary to fill the lot in 30 minutes. Since your rate is in lots/hour, express 30
minutes as 0.5 hours.
r × t = w
↓
y( 121 ) × 0.5 = 1
Solve for y:
12 y×^12 = 1
24 y = 1
y = 24 - B Rate = worktime, so the rate of the first cook, in batches per minute, is 201 , and
the rate of the second cook, in batches per minute, is 101. To get their combined
rate, add up these rates: 101 + 201 = 203. To determine how long it will take the
cooks to produce 3 batches, use the r × t = w formula:
r × t = w
↓
203 t = 3
Solve for t: t = 20 minutes. The question asks for how many hours it will take,
so convert minutes to hours. 20 minutes is^13 of an hour. - C The rate at which the tank fills will be the difference between the rate of the
hose filling the tank and the rate at which the tank empties: 15 liters/second –
10 liters/second = 5 liters/second. Since the question asks for the time at which
the tank will be half full, the work is 100 liters. Now use the r × t = w formula
to solve the problem:
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 35104-GRE-Test-2018_313-462.indd 351 12/05/17 12:04 pm