Absolute value equations

Question

A compact car will drive three miles east, five miles west, and then 13 miles east again. The car 1 gets 40 miles per gallon, and there is 1/4 of a gallon of gas left in the tank. Compute the relative distance and the total distance. Then decide if there is enough fuel for the trip.

Answer 1

Let's say that when moving to the east, your moving in the positive direction.  When moving west, you're moving in the negative direction.

 

     Relative distance = 3 mi - 5 mi + 13 mi = 11 miles east of where the car started

 

In computing total distance, you don't care which direction you travel:

 

     Total distance = |3 mi | + |- 5 mi|  + |13 mi | = 21 mi. 

 

The car gets 40 miles per gallon and it has 4 gallons left, so it can drive 40*4=160 miles.  Since 21 mi < 160 mi, there's more than enough fuel for the trip.