September 26, 2003

work problems

Here are a few typical work and rate problems for the GRE:

Question 1:
Alice and Bebe can finish a job together in 3 hours. If Bebe can do the job herself in 10 hours, what percent of the job does Alice do?

Answer 1:
Let's not use any formulas here. If Bebe can do the job in 10 hours, that means she does 1/10 of the job in 1 hour. We want to know how much work she does in 3 hours, so that's 3/10 of the job in 3 hours. Therefore, Alice does 7/10 of the job in 3 hours (since 10/10 of the job is a entire job). Turn 7/10 into a percentage, and we have 70%. Go Alice!

Question 2:
There are 20 percent part-time employees at Fast Automaton; the rest are full-time employees. At the end of the year 30 percent of the full-time employees received bonuses. If 72 full-time workers received bonuses, how many employees does the Fast Automaton employ?

Answer 2:
We know that 20/100 are part-timers and 80/100 are full-timers at Fast Automaton. We also know that 30/100 of the 80/100 employees = 72.
Here are my equations:
0.20W + 0.80W = W
0.30 (0.80W) = 72
Workout the second equation.
.24W = 72
W = 7200/24 = 300
Therefore, Fast Automaton employs 300 people.

Question 3:
Gloria runs from home to the poolhall at an average speed of 6 miles per hour, and then walks home on the same route at an average speed of 3 miles per hour. If her whole journey took one hour, how many miles is her home from the poolhall?

Answer 3:
From home to poolhall is 6 m/h and from poolhall to home is 3 m/h. We want to know miles, but we know the total trip was 1 hour.

(X miles) / (6 mph) + (X miles) / (3 mph) = 1 hour
(3X hours + 6X hours) / 18 = 1 hour
(3X + 6X) hours = 1 hour * 18
9X hours = 18 hours
X = 2

Therefore, Gloria's home is 2 miles away from the poolhall.

Posted by oneray at September 26, 2003 8:45 AM