Two buses are travelling on the highway from X to Y

Expert replies

guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Mon Jun 24, 2013 1:16 pm

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.

A)36 KM , 3 Hrs 36 Mins
B)36 KM, 3 Hrs 51 Mins
c)24KM, 3 Hrs 50 mins
d)24 KM, 3 hrs 51 mins
e)48 KM, 2 Hrs 51 mins

OA B

Source: Beat The GMAT — Problem Solving | Mon Jun 24, 2013 1:16 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Mon Jun 24, 2013 4:15 pm

Distance = 180kms
Bus A takes 3 hours to cover 180 kms (go from X to Y)
Bus B takes 4.5 hours to go from x to Y
Now Bus A Starts from X at 11:00 AM, reaches Y at 2:00 PM, waits for 15 mins and starts to return to Point X at 2:15 PM
Bus B starts from point X at 11:15Am and until 2:15PM, it covers 40*3 = 120 Kms
AT 2:15PM, 2 buses are 60 Kms apart and their relative speed = 100 kms as they are travelling in opposite directions)
Time it will take Bus A and B to meet = 60 KMS /100 KM/Hr or 36 mins
In 36 mins Bus A will have travelled 36 * 60 / 60 kms = 36 KMS
Therefore the 2 buses meet 36 kms away from Point Y

And the 2 buses will meet at 2:15 + 36 mins = 2:51PM
Time from 11:00Am to 2:51PM = 3 hrs 51 Mins

Ans B

inavdeep: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Sun May 26, 2013 8:52 pm

by inavdeep » Mon Jun 24, 2013 9:29 pm

Option B

vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Tue Jun 25, 2013 1:32 am

Shorter way
at 3;15 hours A will start from Y
now match time and KM from ans choices 3;15 + ;36 = 3;51

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