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 AP stat and probability 1
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shwang
Average Member

USA
11 Posts

Posted - 08/31/2007 :  15:17:27  Show Profile
1. A car travels 20 mph going uphill and 60 mph going downhill. What is its average (arithmetic mean) speed, in miles per hour, if it goes 90 miles uphill and then 90 miles downhill?

WHAT I DID: I didní»t understand the question. Isní»t the speed still 20 mph uphill and 60 mph downhill no matter how long the distance is?

2. If x, y, and z represent three numbers such that y=x+8 and z=y+5, what is the result when the average (arithmetic mean) of the numbers is subtracted from the median of the numbers?

WHAT I DID: I think I have to find the values of x, y, and z, then use those values to find the average and the mean and solve the problem. So when I solve, I get y=x+8 and z=x+13. Is there a way to solve for x and then substitute the value into those two equations to get y and z, or am I supposed to just pick a value for x and find y and z accordingly?

3. How many arrangements of the letters of the word TROUBLE are possible with R as the middle letter?

CHOICES: a) 30 b) 36 c) 120 d) 360 e) 720

WHAT I DID: I can write down all the possibilities but is there an easier way to solve this problem? A formula perhaps? If there is no easier way, how can I write down all the possibilities and make sure I didn't miss any possibilities?
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shwang
Average Member

USA
11 Posts

Posted - 08/31/2007 :  15:27:01  Show Profile
The choices for 1. and 2.

1. CHOICES: a) 36 b) 40 c) 45 d) 48 e) 54

2. CHOICES: a) -2 b) -1 c) 0 d) 1 e) 2
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Mrspi
Advanced Member

USA
998 Posts

Posted - 08/31/2007 :  16:38:53  Show Profile
quote:
Originally posted by shwang

1. A car travels 20 mph going uphill and 60 mph going downhill. What is its average (arithmetic mean) speed, in miles per hour, if it goes 90 miles uphill and then 90 miles downhill?

WHAT I DID: I didní»t understand the question. Isní»t the speed still 20 mph uphill and 60 mph downhill no matter how long the distance is?

2. If x, y, and z represent three numbers such that y=x+8 and z=y+5, what is the result when the average (arithmetic mean) of the numbers is subtracted from the median of the numbers?

WHAT I DID: I think I have to find the values of x, y, and z, then use those values to find the average and the mean and solve the problem. So when I solve, I get y=x+8 and z=x+13. Is there a way to solve for x and then substitute the value into those two equations to get y and z, or am I supposed to just pick a value for x and find y and z accordingly?

3. How many arrangements of the letters of the word TROUBLE are possible with R as the middle letter?

CHOICES: a) 30 b) 36 c) 120 d) 360 e) 720

WHAT I DID: I can write down all the possibilities but is there an easier way to solve this problem? A formula perhaps? If there is no easier way, how can I write down all the possibilities and make sure I didn't miss any possibilities?




1) Average speed = (total distance) / (total time)

The car goes 90 miles UPHILL at 20 mph. How long will this take (recall that time = distance / rate).

The car goes 90 miles DOWNHILL at 60 mph. How long will this take?

What is the total distance traveled?
What is the total time?

Now, divide total distance by total time to get average speed.

2) Using what you have so far, could we not represent the three numbers as x, x + 5, and x + 13? Do you see that these are in order from smallest to largest no matter what value we assign to x?

Now....the median (middle value) is x + 5

Find the average (mean)....[x + (x + 5) + (x + 13)] / 3

Subtract the median from the mean.

3) There are 7 letters in the word "trouble," and the possible arrangements you are to form must have R in the 4th position:

__, __, __, R, __, __, __

That leaves 6 letters from which to choose the first letter, 5 ways to choose the second letter, 4 ways to choose the third letter, 1 way to choose the fourth letter (it's got to be R), 3 ways to choose the fifth letter, 2 ways to choose the sixth letter, and 1 way to choose the seventh letter.

There are 6*5*4*1*3*2*1 possible arrangements.

I hope this helps you.


(edited to correct spelling error)

Edited by - Mrspi on 08/31/2007 17:29:40
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shwang
Average Member

USA
11 Posts

Posted - 08/31/2007 :  17:33:01  Show Profile
Thanks for your reply. This is how I solved it with your help. I solved out everything but number 1 didn't work out.

1. The total distance is 180 and the total time is 6 hours.
When I divide 180 with 6, I get 30, which is not in my answer choices. What did I do wrong?

2. I got x+7 for the mean and when subtrated that from the median, I've got 1 as my answer. Thank you!

3. I got 720 as my answer. Thank you!
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Mrspi
Advanced Member

USA
998 Posts

Posted - 08/31/2007 :  21:18:35  Show Profile
For problem 1....

You go uphill for 90 miles at 20 mph....

time = distance/rate

so uphill time = 90 miles / 20 miles/hr, or 4.5 hours

You go downhill for 90 miles at 60 mph.

time = distance / rate

downhill time = 90 miles / 60 miles/hr, or 1.5 hours

Ok...if the time going uphill is 4.5 hours, and the time going downhill is 1.5 hours, the total time traveled is 4.5 hours + 1.5 hours,
or 6 hours.


Average speed = 180 miles / 6 hours,

or

Average speed = 30 miles / hr

Since this is NOT one of your possible answer choices, I would guess that there is a mistake in the answer choices.


I'd welcome any corrections if I've made a mistake in the solution for this problem.





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