You are here:

Advanced Math/Precalculus

Advertisement

Expert: - 10/12/2010


Question
The sum of two numbers is twice their difference. The larger number is 4 more than twice the smaller. Find the numbers.

Also, I do not understand this word problem:

A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15  min. What is his speed in still air, and how fast is the wind blowing?

Thanks!

Answer
The numbers are x and y.
It is given that x+y = 2(x-y) and x = y+4.

Simplifying the 1st equation gives x+y = 2x-2y => 3y = x.
Putting x = 3y into x = y+4, we get 3y = y + 4, so 2y = 4, or y = 2.
This means that x = 2 + 4 = 6.


Using the physics formula d = rt where d = distance, r = rate,
and t = time, we know that d = 180 mi.

Let the wind be at w and his rate in the plane be s.

The problem gives us (1) 180 = (w-s)2 and (2) 180 = (w+s)1.25
since 1 hour and 15 minutes = 1.25 hours.

These equations can be changed to two more equation by
dividing equation (1) by 2 and dividing equation (2) by 1.25.

This gives (3) 90 = w - s and (4) 144 = w + s.

This puts w in the middle between 144 and 90, so it is (144+90)/2.
Now 144 + 90 = 234, and 234/2 = 117.
Using (3), s is seen to be found by 90 = 117 - s, so s = 27.
Using (4) to check, 90 = 117 - 27, and that is correct,
so the answer is true.

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.