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HELP!! QR questions

Discussion in 'DAT Discussions' started by RozhonDDS, Jul 21, 2006.

  1. RozhonDDS

    7+ Year Member

    Jan 2, 2006
    Likes Received:
    Dental Student
    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
  2. Arsenalista

    Arsenalista Member
    5+ Year Member

    Jan 4, 2006
    Likes Received:
    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!
  3. aranjuez

    aranjuez Member
    7+ Year Member

    Jun 24, 2006
    Likes Received:
    Dental Student


    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

    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.

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