# HELP!! QR questions

#### RozhonDDS

10+ Year Member
7+ Year Member
Well i took calc 1 and 2 and got A's in both of them but it seems like when it comes to reviewing for QR I forget the most obvios things. Please help me with these problems.

1)A painting which is 4ft wide and 5ft long is surrounded by a rectangle dframe 6-inches wide. What percent of the area of the picture and the frame is occupied by the frame?
ANS: 33 1/3

2)If y=(x+2)/(x-3) than which represents x?

ANS: (3y+2)/(y-1)

3)A person travels to work at an average speed of 40mph and returns home at 60 mph. Which of the following in mph is the average speed of entire trip?

ANS: 48

4) 10 is to 2y as 25x is to which of the following?

ANS: 5xy

5) One pump can fill a vat in 10min another can fill it in 15min. How many minutes does it take if they are both operating at the same time?

ANS: 6

#### Arsenalista

##### Member
10+ Year Member
5+ Year Member
3) Imagine that the person travels 120 mi to work.
On the way there, that person takes 3 hours to get there (120 mi/40mph)
On the way back, that person takes 2 hours to return home (120 mi/60 mph).

So the person spends 5 hours in transit, covering 240 miles in total.
240 mi/5 hours = 48 mph

5) Pump #1 can fill 6 vats in an hour. (60 min/10 min per vat = 6)
Pump #2 can fill 4 vats in an hour. (60 min/15 min per vat = 4)

If they fill as many vats as possible in an hour, they will fill 10 vats; one every 6 minutes. (60 min/10 vats = 6 min/vat) Good luck!

#### aranjuez

##### Member
10+ Year Member
7+ Year Member
RozhonDDS said:
Well i took calc 1 and 2 and got A's in both of them but it seems like when it comes to reviewing for QR I forget the most obvios things. Please help me with these problems.

1)A painting which is 4ft wide and 5ft long is surrounded by a rectangle dframe 6-inches wide. What percent of the area of the picture and the frame is occupied by the frame?
ANS: 33 1/3

2)If y=(x+2)/(x-3) than which represents x?

ANS: (3y+2)/(y-1)

3)A person travels to work at an average speed of 40mph and returns home at 60 mph. Which of the following in mph is the average speed of entire trip?

ANS: 48

4) 10 is to 2y as 25x is to which of the following?

ANS: 5xy

5) One pump can fill a vat in 10min another can fill it in 15min. How many minutes does it take if they are both operating at the same time?

ANS: 6

Alright...

1.) Area of the painting is 4ft *5ft = 20 sq. ft
The frame then takes 6 in. on each side... so 4ft+2(6in.) = 5 ft for the new width... and similarly... 5ft+2(6in) = 6ft. ... so 5ft*6ft = 30ft (painting + frame)
30-20 = 10... that's the area of the frame... ratio of the area of the frame to the entire area = 10/30 = 1/3 = 33 1/3 percent

Remember... for that frame, you have to add 6 in. to EACH side... draw it out if you can't see it in your mind's eye.

2.) y = (x+2)/(x-3)
y(x-3) = (x+2)
xy-3y = x+2
xy-x=3y+2
x(y-1)=3y+2
x=(3y+2)/(y-1)

3.) I like to think of these problems with an actual distance in mind. Let's pick 240 mi. to work (one way). To get there takes 40x=240... x = 6 hrs
To come back... 60x=240... x=4 hrs... that's a total of 10 hrs, round trip. Also, round trip is 2*240 mi, which is 480... rate = 480mi/10hrs = 48mph

4.) To get from 10 to 2y, you divide by 5 and multiply that number by y. So if you have 25x, divide by 5 (to get 5x) and then multiply by y, to get 5xy.

5.) This is another one of those problems to do with a number in mind. Say the vat is 30 L. The first pump can do it in 10min, which means it does 3L/min. The second one, 2L/min. Add the two rates together, and you get 5L/min.

5 L/min * y = 30L
y=6 min.

Hope that makes sense. Repost if you need further clarification.

aranjuez