QR questions....please help

[winterhot]

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I have 2 questions that I don't know how to do. Please help me. Thanks in advance.

A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fill the tank if both pipes are open?

a. 45
b. 60
c.75
d. 80
e. 100

Optometry school applicants decreased by 25% during a 4-year period. During the same time, the number of first-year opnenings in optometry school increased by 12%. If the ratio of applicants to first-year student openings had been 3-1, then which of the following would be the approximate ratio at the end of the 4-year period?

a. 1.5-1
b. 2-1
c. 3-2
d. 4-3
e. 6-5

 

[yankees27th]

1st question: Imagine the tank holds 100 gallons. In 30 minutes it would be full from the first pipe. However, the second pipe is going to remove 60 gallons over that time (30/50) times 100. So you fill 40 gallons in 30 minutes. Set up a proportion (30min/40g)=(xmin/100g). x=75minutes. The answer is C.

I have to get to class now. I'll look at the second question later.

 

[peyman2002]

I have 2 questions that I don't know how to do. Please help me. Thanks in advance.

A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fill the tank if both pipes are open?

a. 45
b. 60
c.75
d. 80
e. 100

Optometry school applicants decreased by 25% during a 4-year period. During the same time, the number of first-year opnenings in optometry school increased by 12%. If the ratio of applicants to first-year student openings had been 3-1, then which of the following would be the approximate ratio at the end of the 4-year period?

a. 1.5-1
b. 2-1
c. 3-2
d. 4-3
e. 6-5

choice "b" for your second question. Lets say we had a total of 80 students, 60 Applicat and 20 First year, after incorporating the percentages for each we end up with 45 applicants and 22.5 first year students thus 2:1 ratio.

 

[whateveryoulike]

for the first one:

if one pipe takes 30 minutes to fill the tank, then you could also say that it fills 1/30th of the tank per minute. if the other tank takes 50 minutes to remove the water, then it drains at 1/50th of the tank per minute. if both are going at the same time, its the rate of the 2 together (but remember that the 2nd pipe should be written as a negative since its REMOVING water instead of adding it)

1/30 - 1/50 = 1/75

so the combined rate is 1/75th of the tank per minute, or 75 minutes total.

for the second one:
the original ratio is 3:1
if they say one decreases by 25% and the other increases by 12% then this is the new ratio
3*(.75):1*(1.12)

which is roughly 2:1

 

[winterhot]

thank you so much for your help. i really appreciate it!!!