SOLUTION: a certail truck uses 18 gallons of diesle fuel in traveling 270 miles. in order for the truck to travel the same distance using 10gallons of diesel fuel. by how many miles per gall

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Question 1014695: a certail truck uses 18 gallons of diesle fuel in traveling 270 miles. in order for the truck to travel the same distance using 10gallons of diesel fuel. by how many miles per gallon must the truck's fuel mileage be increased?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Basic uniform rates, fuel efficiency is D%2FV=R for a constant nonzero real number, R. This is a rate comparing distance D to fuel quantity V, volume. Multiplying both sides by V, the relationship is stated D=RV or RV=D.

Assign some variables:
r, fuel efficiency rate MILES per GALLON
x, increase in fuel efficiency needed

This is the description translated into a system of equations.
system%28r%2A18=270%2C%28r%2Bx%29%2A10=270%29

Think about the variables and these two equations and make sense of them. If they seem very understandable, then you know what to do.
Solve the system for r and x. The first equation will give you r; and then use the value found in the second equation to solve for and evaluate x.

The important part of the exercise is to learn to make the system of equations and then to solve it. The actual values for r and x and not very important.