Please help me with this GMATPrep question.
During a car trip, Maria stopped to rest after she traveled ┬╜ of the total distance to here destination. She stopped again after she traveled ┬╝ of the distance remaining between her first stop and her destination, and then she drove the remaining 120 miles to her destination. What was the total distance, in miles, from MariaтАЩs starting point to her destination?
I'm going to take a stab at this one.
Let x = the total number of miles on Maria's trip
.5x = the first half of the trip that she drove before her 1st stop
.5(.25) = .125x = the distance she travelled before her 2nd stop
120 miles = the total number of miles she drove to the destination
You can approach this problem one of two ways: algebraically, and intuitively.
Since we know that 120 miles = 3/4 of 1/2 of the trip (or 3/8ths of the entire trip: 3/4 * 1/2), we can understand that 160 miles is equal to one half of the entire trip. Multiply 160 miles by 2 (2 halves of the trip) and you'll get 320.
You can also solve this algebraically:
.5x + .125x + 120 = x
.625x + 120 = x
120 = .375x
x = 320
Correct answer choice is B: 320.