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

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

by BTGmoderatorLU » Fri Jan 25, 2019 2:38 pm

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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
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by GMATGuruNY » Sat Jan 26, 2019 4:03 am
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
Let d = the number of miles between A and B.

Since Georgia travels the entire d miles between A and B and then an additional 60 miles back toward A, Georgia's distance = d+60.
Since Frank travels all but 60 of the d miles between A and B, Frank's distance = d-60.
Since Georgia's travels 3/2 times as fast as Frank, her distance must be 3/2 times Frank's distance:
d+60 = (3/2)(d-60)
2d+120 = 3(d-60)
2d+120 = 3d-180
300 = d.

The correct answer is E.
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by swerve » Sat Jan 26, 2019 8:03 am
Let the total distance = x.
Distance covered by G = x+60.
Distance covered by F = x-60.

Since the time required to cover the above distance is the same, we have that

Tg = Tf
x+60/1.5s = x-60/s
1.5x -90= x+60
0.5x= 150
x= 300.

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edited

by deloitte247 » Sun Jan 27, 2019 4:52 am
Let total distance covered be = x
Total distance covered by Georgia = x + 60
Total distance covered by Franck = x - 60
Since time required to cover the distance are the same
Time of Georgia = Time of Franck
$$\frac{\left(x+60\right)}{1.5}=\frac{\left(x-60\right)}{1}$$
$$1.5x-90=x+60$$
$$1.5x-x=60+90$$
$$0.5x=150$$
$$\frac{0.5x}{0.5}=\frac{150}{0.5}$$
$$x=300$$

$$answer\ is\ Option\ E$$
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by Scott@TargetTestPrep » Fri Feb 15, 2019 5:16 pm
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

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