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

Question

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 ?

A. 35 mph
B. 45 mph
C. 50 mph
D. 60 mph
E. 70 mph

whiplash2411 · Accepted Answer

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

KarishmaB · Answer

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.

GMATBLACKBELT720 · Answer

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

jlgdr · Answer

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

jlgdr · Answer

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

ThatDudeKnows · Answer

Instead of algebra, let's just Plug In The Answers (PITA). I like trying B and D.

B: Eden travels 45mph. Rex travels 25mph.
Eden travels for 4 hours, so 180 miles. Rex travels for 6 hours, so 150 miles.
Nope.

D: Eden travels 60mph. Rex travels 40mph.
Eden travels for 4 hours, so 240 miles. Rex travels for 6 hours, so 240 miles.
Yep.

Answer choice D.

ThatDudeKnowsPITA

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

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