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Frank and Georgia started traveling from A to B at...

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Frank and Georgia started traveling from A to B at...

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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. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross 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.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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LUANDATO wrote:
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 cross 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 distance between A and B.

Georgia travels the total distance in red:
A------------------------------------------->B
A................................................<-----60-----B

Since Georgia travels the distance between A and B plus an additional 60 miles, Georgia's distance = d+60.

Frank travels the distance in blue:
A----------------------------->.........60.........B
Since Frank travels the distance between A and B except for the last 60 miles, Frank's distance = d-60.

Since Georgia's rate is 3/2 Frank's rate -- and the two travel for the same amount of time -- Georgia's distance must be 3/2 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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LUANDATO wrote:
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. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross 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.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Helps to visualize or draw a diagram.

Calling the distance between A and B, "D", recognize that she has traveled that full distance and then an additional 60 miles back toward A when she meets Frank

So the distance Georgia travels is D+60. Call Frank's speed R, so her speed is 1.5*R. Use D=R*T,

D+60 = 1.5R x T

Over this same time recognize that Frank has traveled to a point 60 miles short of B, so his distance traveled is

D - 60 = R x T

Use this equation to eliminate D = R x T + 60. Substitute this into the first equation:

R x T + 60 + 60 =1.5R x T

Simplify, 0.5R x T = 120 > R x T = 240

See from above that D is R x T +60, so D = 240 + 60 = 300 , E

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LUANDATO wrote:
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. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross 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.

I'm really confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Let's say Georgia's speed is 30 mph and Frank's is 20 mph. (We could have picked any numbers so that Georgia's speed was 1.5 times that of Frank's.) And say they travel for t hours.

Georgia's total distance = 30t
Frank's total distance = 20t

Now we know that Georgia will have covered 120 miles more than Frank. (Frank stops 60 miles short of B. Georgia will cover those 60 miles to B, and then 60 miles back to meet Frank.)
Thus 30t = 20t + 120
10t = 120
t = 12

So Frank's total distance is 20t = 20*12 = 240. If he was 60 miles short of B, then the total distance from A to B is 240 + 60 = 300. The answer is E

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LUANDATO wrote:
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. Whne Georgia arrived at B, she turned right around and returned by the same route. She cross 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
We can let r = Frank’s speed and 1.5r = Georgia’s speed. Also, we can let the distance between A and B = d.

Since they met at 60 miles away from B, we see that the time Frank spent on driving 60 miles less than the distance between A and B is the same as the time Georgia spent on driving 60 miles more than the distance between A and B. Thus we can create the following equation:

(d - 60)/r = (d + 60)/1.5r

1.5r(d - 60) = r(d + 60)

1.5(d - 60) = d + 60

1.5d - 90 = d + 60

0.5d = 150

d = 300

Answer: E

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