Lionel and Ursula are both cycling in the direction of

Question

Lionel and Ursula are both cycling in the direction of Fenton on straight roads at constant speeds. Lionel, who is heading north, is currently twice as far away from Fenton as is Ursula, who is cycling to the west. If neither stops nor changes direction in the course of the day, what is the ratio of the speed of Lionel's bike to that of Ursula's? 

(1) In four hours, Lionel and Ursula will both be 10 miles from Fenton. 
(2) In terms of straight line distance, Ursula's car is currently 25*sqrt(2) miles from Lionel's.

braindancer · Answer

I'd say both together are sufficient. Use (2) to determine their distances from Fenton (you have the right-angled triangle with known hypotenuse and leg ratio - that's enough); then, use (1) to determine speeds.

2times · Answer

IMO  A 

The path is basically rectangular with L& U starting at one vertex and their destination F at the opposite vertex.

so let us assume the breadth of the rectangle = x; pointing north on which L is tarveling
length of the rectangle = y; pointing West on which U is traveling.

so total distance between the starting point & end point is half of perimeter or x+y

now the question says X+Y -DL = 2(X+Y- DU)

where DL & DU give the distance travelled by L & U respectively.

=> X+Y = 2DU - DL......(1)

Now statement 1:

let speed of L = SL; distance covered in 4 hrs = 4SL
let speed of U = SU; distance covered in 4 hrs = 4SU

so.. X+Y -DL -4SL=10
and X+Y -DU - 4SU=10

substituting from (1)

2DU -2DL -4SL =10
& DU-DL -4SU =10

solving SL/SU = 2/1

therefore A can give the ans.

Statement B....
IMO B cannot give the ans alone as it only mentions their current distance and not their speed

 Therefore A 

kevincan OA?

2times · Answer

kevincan,

You mean I got the intial problem construction incorrect or the ans incorrect

kevincan · Answer

I see them at opposite ends of the hypotenuse of a right triangle!

2times · Answer

hummmm.... makes sense; cause in the way i have assumed the road turns, and u mention that they donnot change directions!

prashrash · Answer

If the answer is not C then what is it please ?
From (1), I get the ratio of speeds to be (2x-10)/(x-10).
From (2), I get to solve for x.
Thus, only by combining (1) and (2) I will arrive at a ratio of Ursula's and Leon's speeds.

prashrash · Answer

Stmt 1 says that after 4 hrs, both Ursula and Leon are 10 miles from the destination. Also the q says that Leon was twice as far away as Ursula at the start. If we consider Ursula's distance from destination to be x, the Leon was 2x away from it. After 4 hours, Ursula has travelled x-10 miles. Leon has done 2x-10 miles. (from stmt 1) Speed of Ursula = (x-10)/4 Speed of Leon = (2x-10)/4 Hence ratio = (2x-10)/(x-10). All of this is, of course, assuming that U and L start from the 2 ends of the hypotenuse of a rt triangle with the right angle being formed at destination. That was the only feasible figure, representing their relative direction of travel, that I could come up with (also confirmed by you in your post above

). Is there another possible eqn for the ratios ?

kevincan · Answer

How do we know whether, when they are at equal distances from Fenton, either has already gone through Fenton?

Yurik79 · Answer

tricky one))
I dunno but i think it is E

yezz · Answer

do we need the slope of the hypotynuss of the right angled triangle????

Kevin??

Thanks

soccerfan · Answer

I believe its (A)

From 1) Let the distance of L from kenvin be 2d and speed be u and that of U be d and speed be v
 Now d = speed * time
hence for L after four hours 
(2d - 10)/u = 4 
hence d = (4u +10)/2 ------------- (1)
for U
(d-10)/v = 4 

d = 4v +10 -----(2)

combining 1 and 2 we get the ratio of u and v

From 2)

the distance is a hypotenuse of a rt angled triagnle ..25sqrt(2) = sqrt ( 2d*d) = dsqrt(2)

hence d = 25 , 2d = 50

But this doesnt help much

Hence A

soccerfan · Answer

Fel into the same trap.

On a second thought its (C) both are needed .

kevincan · Answer

OA E: From A, we cannot conclude anything about the ratio of speeds, because we don't know on what side on Fenton the two cities are. Knowing the current distances (from 2) of each will not help.

Lionel and Ursula are both cycling in the direction of

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