Hayden began walking from F to G, a distance of 40 miles, at the same

Question

Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Hayden's walking speed was x miles per hour and Ava's was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?

(A)  \frac{40(x-y)}{x+y}

(B)  40x-\frac{y}{x+y}

(C)  \frac{(x-y)}{x+y}

(D)  \frac{40y}{x+y}

(E)  \frac{40x}{x+y}

Ok. This is how I am solving this.

Hayden's speed = x miles/hr
Ava speed = y miles/hr

Relative speed = (x+y) miles/hr as they are travelling in opposite direction (F to G and G to F)

Total time taken =  \frac{40}{x+y}  ---------------------------

So Hayden will take =  \frac{40x}{x+y} ------------------------- . But not 100% why though? Can someone please help?

Bunuel · Accepted Answer

Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Haydens walking speed was x miles per hour and Avas was y miles per hour, how many miles away from F were they, in terms of x and y, when they met? 
(A)  \frac{40(x-y)}{x+y} 
(B)  \frac{40(x-y)}{x+y} 
(C)  \frac{(x-y)}{x+y} 
(D)  \frac{40y}{x+y} 
(E)  \frac{40x}{x+y}

Combined rate of Hayden and Ava is  x+y  miles per hour, hence they will meet in  time=\frac{distance}{rate}=\frac{40}{x+y}  hours. In  \frac{40}{x+y}  hours Hayden will cover  distance=rate*time=x*\frac{40}{x+y}  miles.

Answer: E.

AbhiJ · Answer

Total time(T) taken is the time for Hayden and Eva to meet. Now you know that Hayden must tavel for time T before they meet. Thus distance Hayden will cover is = Time T * Hayden Speed.

enigma123 · Answer

Thanks Bunuel. But why we are only calculating it for Hayden? That's where I am getting confused buddy.

Bunuel · Answer

Hayden began walking from  F  and we are asked how many miles away from  F  were Hayden and Ava when they met. In 40/(x+y) hours Hayden, at x miles per hour, will cover 40/(x+y)*x miles from  F .

minkathebest · Answer

This is a confusing problem - especially if someone assumes x = y, then choice D is also valid.

SVaidyaraman · Answer

1. Time taken for the two to meet which is also the time walked by Hayden = 40 /x+y hrs
2. Speed of Hayden = x miles/hr
3. Distance traveled by Hayden = 40x / (x+y)

WholeLottaLove · Answer

Hayden began walking from F to G, a distance of 40 miles, at the same time Ava began walking from G to F on the same road. If Haydens walking speed was x miles per hour and Avas was y miles per hour, how many miles away from F were they, in terms of x and y, when they met?

combined speed = x+y miles/hour

time in which it took them to meet = 40/x+y

So, we know that it takes them 40/x+y hours to meet up. The question states that Hayden traveled from F to G and Ava, from G to F. It asks us how far from F (Hayden's starting point) did they meet at. Therefore, to solve for distance (d=r*t) we solve by multiplying Hayden's rate (x) by the time it took them to meet (40/x+y) to get 40x/x+y

ANSWER: E

lastshot · Answer

Still much is left in explanation :

Ans you will get will be same if you multiply Ava rate with time when they meet :

As Distance travel by ava when they meet : y* 40/(x+y)

Now question has asked distance from F i.e. you have to subtract distance travel by ava from 40.

therefore - 40 - (40y/x+y) = on solving you will get 40x/x+y i.e E

Hope i make it clear

PareshGmat · Answer

Refer diagram below;

We require to find d (in terms of x & y)   (how many miles away from F were they)

Setting up the equation

\frac{d}{x} = \frac{40-d}{y}

(x+y)d = 40x

d = \frac{40x}{x+y}

Answer = E

PareshGmat · Answer

Please refer diagram above. There should be no confusion after

effatara · Answer

F------------------------M-------------------------------G
Hayden-----> <------Ava

Hayden starts from Point F, Ava from Pt G and they meet at Pt M. Since the question is "how far from F do they meet", we are required to figure out FM i.e. the distance that Hayden covers  . Since they start walking towards each other at the same time and continue walking until they meet, they take the same amount of time to cover their respective distances  . Therefore, the ratio of their speeds is equal to that of the distances they cover until they meet. T/4, FM:GM=x:y. Since  =40 miles, FM=40x/ . Ans:E.

ashishahujasham · Answer

Can we get this answer by plugging in some values

Sent from my A1601 using  GMAT Club Forum mobile app

effatara · Answer

ashishahujasham
Yes, we can. Let's assume x=20 mph and y=60 mph. Then, FM:GM=20:60=1:3. That is, FM (distance covered by Hayden) is 1/4th the total distance (40 miles). T/4, FM=10 miles. Now, lets plug in the assumed values of 'x' &'y' in FM=40x/(x+y): 
40x20/(20+60)=800/80=10 miles.
I am not sure from your question if that is what you needed explained. If so, glad to have been able to help.

Cbirole · Answer

Since H and E are walking in opposite direction, relative speed will be summation i.e. X+Y
Time required by both of them to meet= 40/Relative speed= 40/(X+Y)
Now from F what distance they will be= Speed*time=X*40/(X+Y)
Ans: E

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Hayden began walking from F to G, a distance of 40 miles, at the same

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