AboutJosh Expertise When I work through problems, I emphasize principles and key ideas which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponentials & Logarithms. Basic Calculus. Probability, Permutations and Combinations. Mathematical Induction. Complex numbers. Physics problems.
Experience
Experience: I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Supplementary Website: See a selection of past questions in my maths repository under "Question Archive"
Education Credentials: Bachelor degree in Engineering Science."Everyone struggles with something."
Question Fuel Efficiency. Last week, Joe’s Electric Service used 110 gallons of gasoline in its two trucks. The large truck was driven 800 miles, and the small truck was driven 600 miles. If the small truck gets twice as many miles per gallon as the large truck, then how many gallons of gasoline did the large truck use?
Answer The fuel used by each truck is given by D(distance driven) times E(efficiency).
Let D be the distance travelled by the big truck.
Let E be the fuel economy of the big trunk. We measure this in gallon/mile.
Let d be the distance travelled by the small truck.
Let e be the fuel economy of the small trunk.
The combined fuel usage is given by:
110 [gallon] = D*E + d*e. ...[Equation 1]
Now, if the small truck is twice as efficient, then e=E/2 (because it uses half the amount of fuel for a given distance).
We also know about the distances travelled by the two trucks: D=800, d=600. So, equation 1 becomes:
110 = 800*E + 600*E/2
110 = 1100*E
E=0.1 [gallon/mile].
Finally, the amount of gasoline used by the big truck is given by D*E = 80 gallon.
