Real world problems with ratio, proportion, direct, inverse and joint variations

Question 1 (easy):

The volume of a pool is 7V liters. A tap pours out y/4 liters of water per minute. Which of the following is the correct expression showing the time in minutes needed to fill 1/5 of the pool?

A. 7V/20y
B. 28V/5y
C. 28y/5V
D. 35y/4V

Question 2 (more difficult):

6 workers of the same capacity are starting to work in the construction of a wall. Every day, one worker is leaving work and the total job is completed in 4 days. If none of the workers left the job, in how many days would they complete the construction of the wall?

A. 1
B. 1.5
C. 2
D. 3

1. B
The total volume of the pool is 7V. 1/5 of the pool is 7V/5. We need to set a simple ratio to find the result:
If the tap pours out y/4 liters of water per 1 minute it pours out 7V/5 liters of water per x minutes

Here, we need to find x. We can do cross multiplication with the values:
y/4 liters  1 minute
7V/5 liters  x minutes
x * y/4 = 7V / 5
x = (7V/5) / (y/4) = (7v/5) * (4/y)
x = 28V/5y

The correct answer is (B).

2.D

This is an inverse ratio problem. There are 6 workers in the beginning. Assume that each worker completes x work per day. Then, 6 workers will complete 6x work per day. On the second day, one worker leaves; so 5x work will be completed. The next day 4x and eventually 3x work will be completed on the 4th day. Since the job is completed in 4 days; 6x + 5x + 4x + 3x = 18x is the total work done. If no one leaves the work; there will be 6x work completed per day. As we know, the total work is 18x, so;

In 18x / 6x = 3 days, the 6 workers would complete the construction of the wall.
The correct answer is (D).