Two buses are travelling on the highway from X to Y .

Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

Round trip from X to Y to X. Distance is 180 km. Round trip = 360 km.

Bus A speed: 60 km/hour
leaves at 11:00 AM
Turns around 15 minutes after it reaches Y
Bus B speed: 40 km/hour
Leaves at 11:15 AM


Bus A reaches Y at 2:00 PM and heads back at 2:15 PM.
By the time bus A heads back, bus B has traveled for 3 hours meaning it has covered 120 km. At 2:15, bus A and bus B are 60 km apart. We can treat closing velocity as a combination of both speeds. In other words, time = distance/rate ===> time = 60/(40km/h + 60 km/h) ===> time = 60km/100km ===> time = .6 hours = 36 minutes. We know that it will take 36 minutes for B to meet A from the time when B has traveled 120 km which means that B will have traveled 3 hours + 36 minutes = 3:36 when they meet. B travels at 40 km/h so in 36 minutes it travels: distance=rate*time ===> distance = 40km/h*.6 ===> it travels an additional 24 km. B is a total of 180-120-24 = 36 km away from Y.

ANSWER: A)36 KM , 3 Hrs 36 Mins

ANSWER: A)36 KM , 3 Hrs 36 Mins

The question asks for how long will they have been traveling for after the departure of A. It takes them 3:36 to meet one another but that is the combined time of A and B. A leaves 15 minutes before B so it has traveled an additional 15 minutes before they meet: 3:36 + :15 = 3:51.

Hey wholelottalove, I think you forgot to add back the 15 minutes that the bus waited at location Y. It drove for 3 hours one way and 36 minutes the other, but there was a respite of 15 minutes, hence why 3:51 and not 3:36.

On a side note, I've never seen an actual GMAT question with multiple components to solve like this one. It's a good question to solve, but it's not a real GMAT question.

Thanks!
-Ron

Thanks! I caught that as soon as you posted your reply. Thanks for the heads up though...stupid mistakes are still wrong answers!

.............
solution:
Time to each Y, 1st bus = 180/60 = 3hours,
then 15 min rest. 2nd bus leaves 15 min later. so it also travels 3 hours.
distance covered by 2nd bus= 40 * 3 = 120
]so from y they are 180-120=60 km apart .

let, they will meet P km from Y after t hours.

now, P = 60 * t
and, 60-P = 40 * t
...............................
(+), 60 = 100t
or, t = 3/5
so p = 60 * 3/5 = 36km (Ans)
total time from the 1st = 3hour and15min+3/5 * 60 = 3hours and 51min (Answer)

Another way to quickly solve is to substitute the answers:

We know bus A goes 1 km per minute. We know bus A left Y at 3:15.

A) 36 km in 21 minutes, impossible
C) 24 km in 35 minutes, impossible
D) 24 km in 36 minutes, impossible
E) 48 km in -24 minutes impossible

B) 36 km in 36 minutes, only possible answer.

By the time first bus gets to Y second bus would have traveled for 3 hours.

Distance covered by bus B

D = speed x time

= 40 x 3

= 120km

Which means distance between the two buses will be 60km.


Time it will take for them to meet

T = 60/100x 60

= 36 mins.

Therefore distance of first bus from Y

60/100 x 60

= 36km.


Time taken for them to meet

3 hours and 36 + 15 mins.

3 hours 51 mins.

GMAT quant instructor Lagos


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