Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 342
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: Two dune buggies start out across the desert at the same time. They
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05 Jan 2015, 14:56
I find that drawing the route helps in such problems.
0_______50________75________________ Let's say that this is the route that has been travelled.
A,B_____A,B________B________________ This is which part they have done.
__________<_______>_________________ This shows the extra that A has to travel
A has travelled for 2 hours: 25*2=50 miles (R*T=D)
B has travelled for 3 hours: 25*3=75 miles
If we create the RTD chart, we can fill in the details using the visual above and the text information:
...........R........T...........D
A........30.......T...........D+25
B........25.......T...........D
How we filled in the chart:
1) We know that B has already travelled 75 miles at 25 miles/hour (rate) and it is stil travelling for an unkown distance D. So, we fill in D beneath the distance and 25 under R.
2) We know that A has still that small part to travel, which as seen in the visual translates to 25 miles. Additionally, it has to travel the distance that D has travelled while A was sleeping under a tree, which is D. So, we fill in D+25 beneath the distance. We also know that its new speed is 30 miles/hour. So, we add 30 under R (rate).
3) We don't know the time of travel, which is T, and it what we are looking for.
From the visual, the row for A gives: 30T=D+25 | T= (D+25) / 30
From the visual, the row for B gives: 25T=D | T= D / 25
We can make these two relationships equal for T: (D+25) / 30 = D / 25 | D = 125
We are going back to the chart to replace D with 125 for A and solve for T:
30T=D+25
30T=125+25
30T= 150
T= 5 ANS E