## Sunday, July 21, 2013

### Word Problem - Distance Problem

Category: Algebra

"Published in Suisun City, California, USA"

The fuel consumption for William's car is 30 mi/gal on the highway and 25 mi/gal in the city. On vacation trip of 400 miles, he used 14 gallons of gasoline. How many highway miles and city miles did he drive on this trip?

Solution:

The given word problem above is about getting the trip distances of highway and city miles that involves the principles of solving two equations, two unkowns because the two fuel consumption for William's car are given. Also, the total vacation trip miles and total gallons of gasoline are given in the problem.

Let x = be the total trip distance of highway miles
y = be the total trip distance of city miles
30 mi/gal = fuel consuption of highway miles
25 mi/gal = fuel consuption of city miles

If the total vacation trip miles is 400 miles, then we can write the first equation as follows

If the total gallons of gasoline is 14 gallons, then we can write the second equation as follows

Multiply both sides of the equation by their Least Common Denominator (LCD) which is 150 as follows

The two unknowns of two linear equations can be solved by elimination method. Consider the two linear equations as follows

Multiply the first equation by 5 and -1 at the second equation, we have

When you add the two equations, x will be eliminated as follows

Substitute the value of y either of the two equations above as follows