Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-09-02 12:47:02

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

mathcounts/amc problems

1. Maria normally spends half an hour driving to work. When her average speed is ten miles per hour slower than usual, the trip takes ten minutes longer. How many miles does she drive to work?

2. Mr. Pillot always rides his bicycle to work, and he begins his ride at the same time every day. If he averages 10 miles per hour, he arrives at work 2 minutes late, but, if he averages 15 miles per hour, he arrives 1 minute early. How many miles does Mr. Pillot ride to work? Express your answer as a decimal to the nearest tenth.

3. Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?

4.For a particular value of k, one root of the equation 5x^2 + kx = 4 is x=2. What is the other root?

(A "root" is a value that makes the equation true, so x=2 is a root of the equation x+3=5.)


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#2 2013-09-02 12:55:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#3 2013-09-05 10:45:19

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: mathcounts/amc problems

did you get the other ones?


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#4 2013-09-05 12:13:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

Have you worked on them?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#5 2013-09-05 12:23:19

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: mathcounts/amc problems

i solved all except for no. 2 and no.3


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#6 2013-09-05 12:31:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

Okay, I will work on them after I get back. I will be offline soon.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#7 2013-09-05 12:35:38

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: mathcounts/amc problems

ok no problem


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#8 2013-09-05 12:40:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

Sorry for the delay but I will get to them.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9 2013-09-06 00:39:30

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,426

Re: mathcounts/amc problems

hi mathstudent2000

2. Mr. Pillot always rides his bicycle to work, and he begins his ride at the same time every day. If he averages 10 miles per hour, he arrives at work 2 minutes late, but, if he averages 15 miles per hour, he arrives 1 minute early. How many miles does Mr. Pillot ride to work? Express your answer as a decimal to the nearest tenth.

3. Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?

My approach for questions like these is to introduce letters for the unknowns, make equations, and then solve.

Q2.  Let distance be D.  Let correct travel time be T in minutes.

Then

D = 10 x (T+2)/60

D = 15 x (T-1)/60

Q3.  Let Rico's speed be V mph. => Donna's speed is 2V/3

V = 2V/3 + 2

etc.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#10 2013-09-06 01:11:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

Hi mathstudent2000;

I will be at a meeting all morning and possibly more. bob bundy has assisted you follow his advice.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#11 2013-09-06 10:50:21

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: mathcounts/amc problems

ok no problem


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#12 2013-09-06 10:56:20

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: mathcounts/amc problems

i got the rico problem now but the pillot problem i'm still not sure how to do with the strategy


Genius is one percent inspiration and ninety-nine percent perspiration

Offline

#13 2013-09-06 14:37:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: mathcounts/amc problems

I solved it in a slightly different way but all roads lead to Rome. Bob has the solution right up there.


D = 10 x (T+2)/60

D = 15 x (T-1)/60

Since both equations equal the same thing we can set the RHS equal to each other.

10 x (T+2)/60 = 15 x (T-1)/60

You will get T = 7.

Solving for T we get:

T = 7. That means he takes 9 minutes at 10 mph and 6 minutes at 15 mph. You should be able to find the distance from that.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB