IQ TEST: Math, Working together, Job, Work problems at the same rate, inverse proportions

1. John can finish the job in 3 hours while Amy can finish the same job in 4 hours. If both work on the same job, how long will they finish?

find:

T = total time if both work together

t1 = time for John to finish the job alone

t2 = time for Amy to finish the job alone

solution:

1/T = 1/t1 + 1/t2


1/T = 1/3 + 1/4

1/T = 7/12

T = 12/7 or 1.7 hours


2. Two carpenters can finish 4 cabinets in 4 hours. If the working rate is the same, how many cabinets can 7 carpenters finish in 24 hours?

find:

J2 = number of cabinets finished by 7 carpenters in 24 hours

given:

m1 = 2 carpenters

t1 = 4 hours

J1 = 4 cabinets

m2 = 7 carpenters

t2 = 24 hours

solution:

m1*t1/J1 = m2*t2/J2


2(4)/4 = 7(24)/J2

2 = 168/J2

J2 = 84 cabinets


3. A factory has an output of 100 units. An additional 20% of output has required an increase of 4 units per worker. If they are working at the same rate, determine the number of workers.


find:

x = number of workers

solution:

OUTPUT = rate * workers

additional output = additional rate * workers


100(0.2) = 4x

20 = 4x

x = 20/4

x = 5


check:

normal capacity:

output = 100

rate = 100/5 = 20 units per worker


at 20% over normal capacity (120 units):

rate = 20 + 4 = 24

output = 24 * 5 = 120 units