Interesting GMATFix Problem-24

[arora007]

On Monday, Hillary and Barrack leave from the same location and travel in different directions. On that day, Hillary travels half as fast as Barrack, but spends 20% more time on the road.
On Tuesday, Barrack remains stationary while Hillary travels 12 miles in a direction perpendicular to her previous day's direction. If Hillary ends up exactly where Barrack is located, how many combined miles did Hillary and Barrack travel on Monday?
A)9
B)15
C)24
D)36
E)48

[goyalsau]

c) 24

[arora007]

The OA is indeed C, but it would be worth it, if there can be a meaningful discussion for all these posts.
Do provide some logical steps as well..with which u solved the problem.

[diebeatsthegmat]

c) 24

i also get the same answer but i just guess, how do you solve it?

[sanabk]

Need to use a right angled triangle for the direction of traveling.

1) Barrack travels on hypo of triangle path with rate=rb and time=t
2) Hillary travels along the base of triangle with rate=0.5rb and time=1.2t
3) Hillary's 12 miles form the height of the traingle

Using HT: (rb*t)^2=(0.5rb*1.2t)^2+(12)^2
=> 0.64(rb*t)^2 = 144
Solving for rb*t=15

Total distance traveled=(rb*t)+(0.6rb*t)=(1.6rb*t)=1.6*15=24.

[Brian@VeritasPrep]

Great problem, everyone (and I like the symbolism of Barack and Hillary finding common ground in the end!).

I'd look at it this way:

First, we can use the R = D/T setup to determine the relative distances of Barack and Hillary.

Barack: R = D/T
Hillary: R/2 (half the rate) = D/(6/5 T) (1/5 more time spent)

Solving for D in Hillary's equation, we can cross-multiply to find that 6/5 TR = 2D, so D = 6/10 D or 3/5 D. She travels 3/5 as far as Barack.

Second, the fact that there is a right angle in this question should stand out as important - right triangles are the single-biggest key to any geometry problem. So let's use Hillary's two travels to form that right angle.

She goes 3/5 D in one direction, then forms a right angle and goes 12 miles in a perpendicular direction. Drawing that out, we'd have a right angle with sides of 3/5 D and 12. The end points are her starting point and her finishing point - and the line between them is Barack's journey of distance D.

So, we now have a right triangle with sides of 3/5 D and 12, and a hypotenuse of D.

Third, let's use Pythagorean Theorem to solve for D:

(3/5 D)^2 + 12^2 = D^2

9/25 D^2 + 144 = D^2

Subtract 9/25 D^2 from both sides to isolate the D terms:

144 = 16/25 D^2

Take the square root of both sides:

12 = 4/5 D

Multiply both sides by 5/4 to isolate D:

15 = D

Now, 15 represents Barack's distance, but we need the total distance, which also includes 3/5 of Barack's distance (which is Hillary's). 15 + 9 = 24, and that's why the correct answer is C.

[GMATGuruNY]

On Monday, Hillary and Barrack leave from the same location and travel in different directions. On that day, Hillary travels half as fast as Barrack, but spends 20% more time on the road.
On Tuesday, Barrack remains stationary while Hillary travels 12 miles in a direction perpendicular to her previous day's direction. If Hillary ends up exactly where Barrack is located, how many combined miles did Hillary and Barrack travel on Monday?
A)9
B)15
C)24
D)36
E)48

Let's determine the ratio of the distances traveled on Monday. We can do this by plugging in our own values.

B = 2 miles/hour
H = 1 mile/hour (Since her rate is 1/2 as fast)
B travels for 10 hours: 10*2 = 20 miles.
H travels for 10 + .2*10 = 12 hours (because she travels for 20% longer). So she travels 12*1 = 12 miles
Ratios of the distances is H:B = 12:20 = 3:5.

This means that the distances form the sides of a 3:4:5 triangle or a multiple of this triangle:
3:4:5
6:8:10
9:12:15
etc.

Since H's distance on Tuesday = 12, the three distances form the sides of a 9:12:15 triangle.
Total distance traveled on Monday = 9+15 = 24.

The correct answer is C.

[diebeatsthegmat]

On Monday, Hillary and Barrack leave from the same location and travel in different directions. On that day, Hillary travels half as fast as Barrack, but spends 20% more time on the road.
On Tuesday, Barrack remains stationary while Hillary travels 12 miles in a direction perpendicular to her previous day's direction. If Hillary ends up exactly where Barrack is located, how many combined miles did Hillary and Barrack travel on Monday?
A)9
B)15
C)24
D)36
E)48

Let's determine the ratio of the distances traveled on Monday. We can do this by plugging in our own values.

B = 2 miles/hour
H = 1 mile/hour (Since her rate is 1/2 as fast)
B travels for 10 hours: 10*2 = 20 miles.
H travels for 10 + .2*10 = 12 hours (because she travels for 20% longer). So she travels 12*1 = 12 miles
Ratios of the distances is H:B = 12:20 = 3:5.

This means that the distances form the sides of a 3:4:5 triangle or a multiple of this triangle:
3:4:5
6:8:10
9:12:15
etc.

Since H's distance on Tuesday = 12, the three distances form the sides of a 9:12:15 triangle.
Total distance traveled on Monday = 9+15 = 24.

The correct answer is C.

ohh so nice... thought the same way....
thanks a lot