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# At what rate must Eden travel to overtake Rex, who is travel

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Manager
Joined: 17 Nov 2009
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At what rate must Eden travel to overtake Rex, who is travel [#permalink]

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18 Jun 2010, 09:05
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At what rate must Eden travel to overtake Rex, who is traveling at a rate 20 mph slower than Eden. If Eden starts 2 hours after Rex and wants to overtake him in 4 hours...

[Reveal] Spoiler:
Eden should travel at 60 mph
Intern
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Schools: Wharton, Stanford, MIT, NYU, Columbia, LBS, Berkeley (MFE program)
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Re: RTD Problem [#permalink]

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18 Jun 2010, 09:58
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This problem tripped me up for a bit. Def. didn't solve it in time.

We have to account for the distance Rex covers while Eden is not moving AND while Eden is moving.

Say Eden's speed is X. This means Rex is X-20. Distance covered in 2hrs -> 2(x-20)

Now we know that T=D/S & 4 is the total number of hours needed to catch up.

4= (4(x-20)+2(x-20))/x. The 4(x-20) is the distance traveled by Rex when Eden is moving.

x= 60
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Re: RTD Problem [#permalink]

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18 Jun 2010, 10:27
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agnok wrote:
At what rate must Eden travel to overtake Rex, who is traveling at a rate 20 mph slower than Eden. If Eden starts 2 hours after Rex and wants to overtake him in 4 hours...

Please show steps to solve

Answer Eden should travel at 60 mph

So let us assume the following:

Speed of Eden = x
Speed of Rex = x-20

To find out how long Rex has been traveling we must piece together two pieces of info: The fact that he started two hours before Eden and that Eden travels for 4 hours before he catches up with Rex.

So:

Travel time for Rex = 6 hours
Travel time for Eden = 4 hours

Now the distance they've traveled is the same, so we have:

$$(x)(4) = (x-20)(6)$$

Solving this we get

$$4x = 6x - 120$$

$$2x = 120$$

x = $$\frac {120}{2} = 60$$

Hope this helps
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Joined: 06 Sep 2013
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Concentration: Finance
Re: RTD Problem [#permalink]

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31 Dec 2013, 08:09
agnok wrote:
At what rate must Eden travel to overtake Rex, who is traveling at a rate 20 mph slower than Eden. If Eden starts 2 hours after Rex and wants to overtake him in 4 hours...

Please show steps to solve

Answer Eden should travel at 60 mph

Check this out we want to know the following

(E-R)(4) = 2R

This means that 'E-R' is the relative speed at which E will travel faster than Rex to overtake him.
4 hours is the required time

The distance is 2R because that's what Rex traveled in the two hour headstart

Therefore solving we get 2E = 3R

Now we are also told that R = E-20

So we can replace and one will get E = 60

Hope it helps!
Cheers!

J
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Joined: 06 Sep 2013
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Concentration: Finance
Re: RTD Problem [#permalink]

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10 Feb 2014, 12:33
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jlgdr wrote:
agnok wrote:
At what rate must Eden travel to overtake Rex, who is traveling at a rate 20 mph slower than Eden. If Eden starts 2 hours after Rex and wants to overtake him in 4 hours...

Please show steps to solve

Answer Eden should travel at 60 mph

Check this out we want to know the following

(E-R)(4) = 2R

This means that 'E-R' is the relative speed at which E will travel faster than Rex to overtake him.
4 hours is the required time

The distance is 2R because that's what Rex traveled in the two hour headstart

Therefore solving we get 2E = 3R

Now we are also told that R = E-20

So we can replace and one will get E = 60

Hope it helps!
Cheers!

J

Here's another way to solve this:

E is X, Therefore R (X-20). The distance traveled by Rex in 2 hrs is 2x - 40.
We need Eden to overtake him in 4 hrs.

Thus, 4(x-(x-20)) = 2x - 40. Solving we get that x =60.

Hope this helps
Cheers
J
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Joined: 16 Oct 2010
Posts: 7934
Location: Pune, India
Re: At what rate must Eden travel to overtake Rex, who is travel [#permalink]

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10 Feb 2014, 21:20
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agnok wrote:
At what rate must Eden travel to overtake Rex, who is traveling at a rate 20 mph slower than Eden. If Eden starts 2 hours after Rex and wants to overtake him in 4 hours...

[Reveal] Spoiler:
Eden should travel at 60 mph

You can also do it without taking any variables but using some logic:

Eden travels 20 mph faster than Rex so he covers 20 miles extra every hour. Eden will overtake Rex in 4 hrs means he will cover an extra 80 miles in this time. Hence, in the 2 hrs that Rex traveled alone, he must have covered 80 miles since this is what Eden needs to cover extra later to catch up with him (using the concept of relative speed and distance). Since Rex covered 80 miles in 2 hrs, his speed must be 40 mph. Eden travels 20 mph faster than Rex so he travels at 60 mph.
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Re: At what rate must Eden travel to overtake Rex, who is travel [#permalink]

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24 Jun 2015, 16:41
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Re: At what rate must Eden travel to overtake Rex, who is travel [#permalink]

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13 Jul 2016, 23:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: At what rate must Eden travel to overtake Rex, who is travel [#permalink]

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13 Aug 2017, 13:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: At what rate must Eden travel to overtake Rex, who is travel   [#permalink] 13 Aug 2017, 13:15
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# At what rate must Eden travel to overtake Rex, who is travel

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