There are 2 cities A & B in a different time-zones.A plane flying at usual speed leaves A at 6 am of its local time and reaches B at 3pm of B's local time.Another plane leaves B at 3pm of its local time and reaches A at 4pm of A's local time.If a plane leaves A at 9am of its local time at its usual speed ,and at same instance another plane leaves B at 2\3rd of the usual speed then what will be the local time of the place where they cross each other.(asuume time-zone change is proportional to the distance). |
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whats the answer ??..i m getting it 12-00 am at location A and 4pm at B..a time gap of 4 hrs..plz do tell me whether its correct or not!
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ya time gap z 4hr.but d question z when they r crossing each other? plz send me the detailed xplanation.
since the time change varies with distance,so let change in time t=k*d where d is the total distance and k being the constant of proportionality. Then, at 6am in location A,the time at B will be (6+kd) hrs. so the time taken for the plane to cover distance 'd' is 15.00( 3pm)-(6+k*d)=9-k*d. similarly when leaving from B,time taken =16.00(4pm)-(15-k*d)=1+k*d. since the speeds r same,so 9-k*d=1+k*d
therefor,k*d=4
i.e. the time gap is 4hrs and speed of the plane =d/(1+k*d)=d/5.Hence, the plane leaving at 9-00 am from A (i.e. 9+4=13-00 hrs at B) will meet the plane leaving from B satisfying the condition :
t*d/5 +t*2/3*d/5=d
where the t is the time of meeting...solving we get, t=3 hrs. hence,the time of meeting will b 9+3 =12-00 at A and similarly 13+3=16-00 hrs at B.
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hi arnab,
excellent solution.... :-)
but the local time at where they cross each other will be 15-00 right??
I think the local time of they will meet is 14:24 min.........can you plz verify ......
YA NEELAY U R ABSOLUTELY RIGHT. IT Z 2.24 .CAN U XPLAIN HOPW U DID IT?
AS WE KNOW TIME DIFFERENCA= 4 HOURS
AND TOTAL JOURNEY TIME IS 5 HOUR AT CONSTANT SPEED
HENCE IF PLANE LEAVE CITY A AT SPEED X THEN ,THEN ANOTHER PLANE LEAVE CITY B AT 2/3X SPEED.
THAT MEANS THEY ARE GOING TO MEET AT DISTANCE WHICH IS IN RATIO OF 3:2 THUS PLANE A HAS TRAVEELED 3 HOURS AT CONSTANT SPEED . THUS IF WE LOOK AT FROM POINT OF A(TIME ) ...... PLANE WILL MEET AFTER 3 HOURS THUS GOING TO MEET AT 12:00
NOW AS TIME ZONE IS PROPORTIONATE TO DISTANCE.....
IT IS ALSO IN THE RAIO OF 3:2
THUS AS TOTAL TIME DIFFERENCE IS 4 HOURS AND DISTANCE IS 5 HOUR ,THEN EVERY HOUR TIME GAIN WILL BE 4/5 HOURS.....
THUS AFTER 3 HOUR IT WILL GAIN 3*4/5 = 2.4 HOURS THAT MEANS 2 HOURS AND .4 * 60 = 2 HOURS AND 24 MIN.......
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