I find this approach simple

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

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.

i get five too but the correct answer is C 2.5 that's why i posted here, to see if someone could show how 2.5 was arrived. This is from an old paper test that doesn't provide an explanation.

WHEN B STARTS AFTER 1 HR REST A WOULD HAVE TRAVELED 25KM

HERE ARE DISTANCES TRAVELED ACCORDING TO TIME



SO ANSWER IS E.

E for me too....!!!!

it takes 5 hours for A to reach B.
the answer should be E.

5 makes complete sense. Catching up by 5 every hour. 25/5 = 5. E.

thanks for the input, i guess answer must be E.

all of your input has really helped.

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
_________________

Both A & B have travelled at same rate 25mph for 2hrs...so they have covered 50miles equally...thats not the question right now

A takes rest for 1 hr and by then since B is still travelling, B has covered 75miles...

After 2 hrs, if we consider both A & B ( with A travelling at 30mph and an hour late, B travelling at 25mph + 1 more hr than A) we need to find out when they will meet "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?"

so
Hours 1 2 3 4 5 6
A 25 50 B 80 120 150
B 25 50 75 100 125 150

so somewhere between 4th and 5th hr from starting they meet
and after first 2 hrs, means 2.5(approx) from 2nd hr...

I Think Your approach is wrong, if you watch keenly the distance traveled by A from 4th hour to 5th hour is 80 to 120, as per question the difference between distance must be 25 or 30 how could you get 40.

Hi harshavmrg,

Your reasoning is right but you made a minor mistake
Hours 1 2 3 4 5 6
A 25 50 B 80 110 140 170 200
B 25 50 75 100 125 150 175 200

and not

Hours 1 2 3 4 5 6
A 25 50 B 80 120 150
B 25 50 75 100 125 150

Thus by any method answer has to be 5hrs
Answer E

I got C (2.5 hours). Can someone please double check for me? Bunuel, quick help please!!

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

Yes, I added something to Buggy B's distance which I should not have. Silly mistake. Thanks for response though.

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

Hey Bunuel,
Can you please advice?I got E as answer but OA is C.

The correct answer is E, not C. Edited the original post.
_________________

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.