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January 18th, 2010, 10:20 PM   #1
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ACT type of math questions, formulas?

Hello,

I am taking the ACT to go to my local state school. I got an A in college algebra in high school, but that was years ago. Any help with these problems & their formulas is appreciated. I'm sure you guys won't find them difficult but I don't remember how to solve these.

1. If Sally can paint a house in 4 hours, and John paint the same house in 6 hours, how long will it take them to pain the house together???? A – 2hr 24min


2. If 300 jellybeans cost you x dollars, how many jellybeans can you purchase for 50 cents at the same rate???? (I think my answer sheet said answer is 150/x. Doesn’t make sense to me.)


3. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking??? A – I think it's 7.5hrs, any formula?


4. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ˝ hours. How quickly can all three fill the pool together?


5. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?


6. Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?


7. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph? (Think book said answer is 500, any formula?)


8. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high with the lid still being able to be closed?


9. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tiles cost $8.91 per square yard?


10. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your head from the top of the tree in a straight line?


11. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?


12. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging your flower bed cost?


13. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?


14. If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet, what is the width?
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January 18th, 2010, 11:44 PM   #2
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Re: ACT type of math questions, formulas?

They're all quite similar, so I'll show a few.

Quote:
1. If Sally can paint a house in 4 hours, and John paint the same house in 6 hours, how long will it take them to paint the house together?
Sally paints 1/4 of the house per hour, John paints 1/6 per hour. Working together they paint 1/4 + 1/6 = 3/12 + 2/12 or 5/12 per hour. So the whole house will take 12/5 hours.

Quote:
2. If 300 jellybeans cost you x dollars, how many jellybeans can you purchase for 50 cents at the same rate?
How many for $x? 300. How many for $1? 300/x. Halve that to get 150/x.

Quote:
3. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
When the second cyclist begins (t=0), the first has travelled 18 miles. Now t hours later, the first will have gone 18+6t, while the second will have gone 10t miles. So solve 18+6t = 10t for t.

Q4,5,6,13. Similar to Q1.

Q7,10. Yes there's a formula, google "Pythagoras theorem."

Q8,9,12,14. Should be easy enough if you draw diagrams.

Q11. The round trip took x/10 + x/8 hours. That's equal to x(1/10 + 1/ = x(18/80) = 9x/40 hours. So his average speed was distance / time = x / (9x/40) = 40/9 mph.

Now have a go at Q4. Start with "Jim fills 1/30 of the pool in one minute..."
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March 22nd, 2010, 12:32 PM   #3
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Re: ACT type of math questions, formulas?

If you're looking for a complete list of ACT math formulas, check out this website.
http://www.actmathformulas.com/
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