A and B start from Opladen and Cologne respectively at the

Question

A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?

(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes

(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes

Found this question on veritas gmat blog. Could not undertand their solution. I was trying to solve the question using algebra and assigning variables but could not get the answer.

saurabhprashar · Accepted Answer

OK. So, Let Speed of A=Va and Speed of B= Vb. Also, they meet after travelling for t minutes. 
Hence, Va*t = distance travelled by A before meeting B ( which happens to be the same as distance travelled by B after meeting and reaching Cologne in 90 mins )
Vb*t = distance travelled by B before meeting A ( which happens to be the same as distance travelled by A after meeting and reaching Opladen in 40 mins )

Hence, 90 mins = Va*t/ Vb = > Va/Vb= 90/t
and 40 mins = Vb*t /Va => Va/Vb = t/40

Hence, 90/t=t/40
t^2 = 3600
t=60 mins
Hence, total time for which A travels = t+40 = 60 + 40 = 1 hours and 40 mins.

GMATGuruNY · Answer

When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same. If A takes 1/2 as long as B to travel 10 miles, then A will take 1/2 as long as B to travel 1000 miles. If A takes 3 times as long as B to travel 500 miles, then A will take three times as long as B to travel 2 miles. Let M = the meeting point. Let t = the time for A and B each to travel to M. Train A: O ----- t -----> M ----> 40 -----> C Train B: O <---- 90 ---- M <----- t ------- C Since A takes t minutes to travel the blue portion, while B takes 90 minutes, the time ratio for A and B to travel the blue portion = t/90. Since A takes 40 minutes to travel the red portion, while B takes t minutes, the time ratio for A and B to travel the red portion = 40/t. Since the time ratio in each case must be the same, we get: t/90 = 40/t t² = 3600 t = 60. Thus: A's total time = t+40 = 60+40 = 100 minutes = 1 hour 40 minutes. D .

AMITAGARWAL2 · Answer

v1 and V2 are speeds. 
v1.t /90 = v2

v2.t/40 = v1
v1/v2 = 3/2
which train A would 90. 2/3 mins to cover the same distance

40 + 60 = 100 mins

SVaidyaraman · Answer

1. If before meeting they had traveled equal distance they would have taken equal time before and after meeting. If A had traveled more distance before meeting, then it means it had traveled faster and then would take less time after meeting to reach its destination.
2. If A traveled let us say 200km before meeting, and B had traveled 50 km before the meeting i.,e A had traveled x times more , in this case 4 times more, then after the meeting A by itself would travel 1/x of 200 km i.e, 50 km after the meeting and B would travel x times more x * 50 = 4*50=200km after the meeting.
3. The time taken by A decreases after the meeting by 1/x and the time taken by B increases after the meeting by 1/x. 
4. In our case, we know the ratio of the time taken by the A and B after the meeting are 1:2.25 min resp. So we have from (3), the ratio of the time taken by A and B before meeting as 1*x : 2.25/x . Because the time taken before meeting is equal 1*x =2.25/x . So x=1.5. That is the time taken before the meeting for A is 40*1.5=60 min 
5. So totally 60 +40= 100 min for A to travel the distance

Udai · Answer

other approach 
t-time taken for A&B to meet
(Va+Vb)t=Va*40+Vb*90;
Va(t-40)=Vb(90-t)
This means 40<t<90
so ans will be 40+t
Only D fits this eqn

gracie · Answer

let t=time to meeting
t/40=90/t
t=60 minutes
60+40=1 hour 40 minutes

sytabish · Answer

Hi  gracie

Can u please explain the method used to solve?

Thanks!

gracie · Answer

Hi sytabish,
Distance varies directly with time. The ratio between the distance from O to meeting and the distance from meeting to C equals 
the ratio between the time from O to meeting and the time from meeting to C, or
distance from O to m/distance from m to C=t/40=90/t
You can confirm these relationships by plugging in a speed of 60 mph for A, 40 mph for B, and a total distance of 100 miles.
I hope this helps.
gracie

erson83 · Answer

let Sa = speed of A.
Sb = speed of B.
Da = distance travelled by A till time t.
Db = distance travelled by B till time t.
t = time the two object collide.

Sa = Db / (2/3) **2/3 = 40 mins
Sb = Da / (3/2) **3/2 = 90 mins

since at time t = Da / Sa = Db / Sb

Da^2 = Db^2 (9/4) 
Da = (3/2) Db

t = (Da + Db) / Sa
 = (3/2) Db + Db / Sa
 = 5/3 hrs.
 = 100 mins.

Mahmud6 · Answer

Would you please explain this t/40=90/t? Why t is in both denominator and numerator? OK got it from https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... -formulas/

avinsethi · Answer

Hi guys, I'm facing a lot of problem with these questions. Where can get proper material to understand the basics of these problems and practice?

Bunuel · Answer

Theory on Distance/Rate Problems: https://gmatclub.com/forum/distance-spee ... 87481.html All DS Distance/Rate Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=44 All PS Distance/Rate Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=64 For more on relative speed, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... elatively/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/08 ... -speeding/ Hope it helps.

Mo2men · Answer

Dear  GMATGuruNY

I had the same result but based on the time is reciprocal with speed.

Let T= time to meeting point, VA=speed of A, VB = speed of B

VA/VB = 90/40 = 3x/2x

Total distance = VA*T + VB *T = 5x * T...........1

But 
Total distance = VA (T+40) = 3x * T + 120x.......2

By equating 1& 2

5x * T = 3x * T + 120x............cancel x

5 * T = 3 * T + 120

2T = 120......T =60 minutes

Then, A will take 1 hour & 40 minutes to reach its distance.

Is my assumption highlighted valid? or is coincidence in this question?

Thanks in advance

GMATGuruNY · Answer

The red portion is incorrect:
 \frac{90}{40} = \frac{9}{4}

The ratio above does not accurately reflect the information given in the prompt.
My earlier solution yields t=60.
Thus:
A's total time = t+40 = 60+40 = 100 minutes
B's total time = 90+t = 90+60 = 150 minutes
Since the time ratio for A and B  = \frac{100}{150} = \frac{2}{3} , the rate ratio for A and B =  \frac{3}{2} 
 \frac{9}{4}  does not accurately reflect the rate ratio for A and B.

Mo2men · Answer

Thanks a lot for explanation.

adewale223 · Answer

Let speed of A be x and speed of B is y

and let t be time the two cars meet.

Distance covered by B after meeting = 90y

Distance covered by A after meeting = 40x

So tx = 90y

ty = 40x

tx t xy = 3600xy

txt = 3600
t = 60.

So time taken by A to cover entire distance = 60 + 40 = 100minutes

1 hour 40 minutes. Answer choice D

https://www.teacheron.com/tutor-profile/8tG7?r=8tG7

Mizan383838 · Answer

Ratio of A and B speed: 3x:2x
Suppose, they meet after 1 'a' hours.

Now,

3ax + 3x×40/60= 2ax + 2x × 90/60

Posted from my mobile device

Natansha · Answer

Hi  KarishmaB  , could you please explain the logic behind t/40=90/t, why is the time ratio not 40/90?

KarishmaB · Answer

This is what is given:

The distance from Opladen to M, A takes t mins and B takes 90 mins to cover. So their speeds are in the ratio 90 : t (same distance so ratio of speeds is inverse of ratio of time taken)
The distance from M to Cologne, A takes 40 mins and B takes t mins to cover. So their speeds are also in the ratio t : 40 (same distance so ratio of speeds is inverse of ratio of time taken)

Of course both are the ratio of their speeds A: B so both are the same ratio.
Hence

\frac{90}{t} = \frac{t}{40}

which means t = 60 mins

So A took 1 hour and 40 mins to cover the distance from Opladen to Cologne.

Answer (D)

A and B start from Opladen and Cologne respectively at the

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