Two dune buggies start out across the desert at the same time. They

Question

Two dune buggies start out across the desert at the same time. They drive in a straight line at 25 miles per hour for two hours. Dune buggy A then stops for an hour while dune buggie B continues on at the same steady rate. After and hour, buggy A begins to moving again in the same straight line as B, but this time at a constant speed of 30 miles per hour. If both Dune buggies hold their rates and drive in the same line, how long, in hours, will it take for A to catch up to B?

A. 1
B. 2
C. 2.5
D. 4
E. 5

i calculated how far both buggies drove for the first two hours:
D=Rate x Time
25 miles/hr x 2hrs = 50 miles

then while Buggy A stopped for 1 hour, buggy B drove another 25 miles
so Buggy A is behind by 25 miles when it started and since buggy A is now at 30 miles per hour,

30MPH-25MPH = 5 miles per hour more that buggy A will be gaining on buggy B with each hour.

so it will take Buggy A 5hrs to catch up or make up 25 miles lost or 5 x 5, but the correct answer is

C)2.5

how come? 
if there is a better approach to solving this problem, please advise.

thank you for your help.

ENAFEX · Accepted Answer

I find this approach simple

Time to Catchup = (Distance Between the A and B)/Relative Speed
= Distance/A-B
=25/5
=5

LalaB · Answer

Since A will reach B, some time later their distances will be the same. so, it means that- 
25(t+1)=30t
t=5 h

nfjet · Answer

I'm pretty sure the answer is E. Distance=rate x time. Rate for B=25. Rate for A=30. At what point will they have traveled the same distance, set both equal to each other while adding 25 to B since B was 1 hour ahead and 25mphx1hr=25miles. time=t. (Bxt)+25=Axt. And from there I get 5.

PareshGmat · Answer

Moderators: The "timer bar" along with correct answer is not showing up for this question.

Can you please instate it??

Thanks

"Resting period" of Buggy A is 01 Hour, in which Buggy B travels 25 kms further until Buggy A restarts.

Say Buggy B moves further "x" (after 25 kms mark) when it is catched up by A

Distance for A = 25+x

Speed of A = 30

Distance for B = x

Speed of B = 25

\frac{25+x}{30} = \frac{x}{25}

x = 125

Total distance from A's resting point = 125+25 = 150

Time required  = \frac{150}{30} = 5

Answer = E

pacifist85 · Answer

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

Nadiuska · Answer

A and B will meet when they'll have driven the same distance.
Until A stops both A and B drive at the same speed, so no need to worry about that. After A stops for 1 hour, so when A reaches B, their distances should be equal, that leads us to form the equation 30(T-1)=25T;30T-30=25T; T=6. So after 6 hours, they'll meet, but remember that A rested for 1 hours so 6-1 = 5. It'll take A 5 hours to reach B.

gracie · Answer

after 3 hours A is 25 miles behind B and gaining 5 miles per hour
25/5=5 hours

shwetasood · Answer

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 How is x=125 ? i can't seem to understand that.

Bunuel · Answer

\frac{25+x}{30} = \frac{x}{25}

(25+x)25=30x

25*25+25x=30x

25*25=5x

5*25=x

125=x

Hope it's clear.

bumpbot · Answer

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