Frank and Georgia started traveling from A to B at the same

BTGmoderatorLU wrote:Source: Magoosh

Frank and Georgia started traveling from A to B at the same time. Georgia’s constant speed was 1.5 times Frank’s constant speed. When Georgia arrived at B, she turned right around and returned by the same route. She crosses paths with Frank, who still was coming toward B when they were 60 miles away from B. How far away are A and B?

A. 72 miles
B. 120 miles
C. 144 miles
D. 240 miles
E. 300 miles

The OA is E

We can let r = Frank’s speed, and thus 1.5r = Georgia’s speed. Furthermore, we can let d = the distance between A and B and t = the time Frank has traveled from A to B when he’s still 60 miles from B. Therefore, we can create the following equations:

rt + 60 = d (since Frank has 60 miles more to go to reach B)

and

(1.5r)t - rt = 120 (since when Georgia meets Frank, she has traveled 60 x 2 = 120 miles more than
Frank)

Simplifying the last equation, we have:

0.5rt = 120

rt = 240

Substituting this into the first equation, we have:

240 + 60 = d

d = 300

Answer: E