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Basic Math/A horribly confusing distance question :-(

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Expert: Michael Tadesse - 8/8/2009


Question
Please could you help me answer the following question. It is driving me insane!! Thank you so much in advance.

The distance from Manchester to Oxford is 270km. One day, road works on the M6 meant that my average speed was 10km/h less than I had anticipated and so I arrived 18 minutes later than planned.

Taking x km/h as the anticipated average speed:

1) Write down an expression in x for the anticipated and actual times of the journey.

2) Form an equation in x and solve it.

3) Find the time of my arrival in Oxford if I left home at 10am.

Answer
Problem #1
The distance from Manchester to Oxford is 270km. One day, road works on the M6 meant that my average speed was 10km/h less than I had anticipated and so I arrived 18 minutes later than planned.

Taking x km/h as the anticipated average speed:

1) Write down an expression in x for the anticipated and actual times of the journey.

2) Form an equation in x and solve it.

3) Find the time of my arrival in Oxford if I left home at 10am.

Solution
Hina it is nice to meet you. It is easy and simple just follow my steps and you will find yourself mastered with such kinds of questions. Without more ado let’s get back to work.
First, Observe that with whatever speed you go, the distance you cover from Manchester to Oxford never changes and it is 270km. putting this in mathematics:
X*T = 270 (where x is the anticipated average speed, T the time taken in hour.)
Second, when you decrease your speed, the time you take to cover the distance increases.
(X-10)*(T+0.3) = 270 (change 18 minute to hour)

Now it is a matter of solving the quadratic equation.
Distributing the second equation you get:
XT – 10T + 0.3X -3 = 270 (but XT is 270 and cancels out the 270 in the right side)
0.3X -3 = 10T
X = (100/3) T + 10
From the first equation we can get:
X = 270/T
Now substituting the latter equation in the former one you can get:
0 = T2 + 0.3T – 8.1
Applying the quadratic formula the value of T can be calculated and it is
T = 2.7hr (162 min), X = 100km/h
Therefore if you left your home at 10 AM, you will arrive at 6.42 PM (after 2 hours and 42 minutes)  

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Michael Tadesse

Expertise

I can answer questions regarding Relations, linear functions and equations, Squares and square roots, Translation and Similarity, Special Properties of Right Angled Triangles, Measurement of Area and Volume, algebra. I can also answer questions related to Pre calculus, Limits and Continuity, Derivatives Applications of Derivatives, High school math in general. I can’t answer questions of the following type. Power Series, Multiple Integrals, Fourier series, Vector valued Functions.

Experience

I love mathematics as it is the mother of all sciences. I had an outstanding math results while I was in school. The tradition continues while I am in university. I have been helping elementary school Students for the past five years with mathematics problems. In fact, I have a brother who is four years younger than me I usually help him to understand what the crux of the question is before trying to solve it. He loves math very much, he is indeed one of the top scorers form his class in Mathematics. I didn’t stop helping my younger relatives after I joined the Engineering campus and I am more than ready to help anyone with my skill.

Education/Credentials
I have a high school diploma with a 3.97 GPA; I also have many merit certificates granted for my outstanding results in high school math. I won a merit certificate for my participation in the Black Month Essay Contest. I took two different National Examinations in 2006 and 2007. In the former Exam I got 9As which includes Mathematics. I also have a score of 90 out of hundred in the later Examination which is the toughest known in Ethiopia. So you don’t have to worry about my ability to help my clients.

Past/Present Clients
I have never had an online client but I was helping students coming to me for assistance in Mathematics.

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