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06 Dec 2020, 07:21
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before meeting point
let the time traveled by both a & b till meeting point is T mins
Let speed A = a, distance travelled by A in T mins = a*T
let speed B = b, distance travelled by B in T mins = b*T
after meeting point
A reached NY in 40 min at speed 'a':- distance = time * speed = 40*a
B reached Boston in 90 mins at speed 'b':- Distance = 90*b
distance travelled by A after meeting point = distance travelled by B before meeting point
therefore
b*T = 40*a.....................(1)
similarly a*T = 90*b.........(2)
multiply (1) and (2)
a*T * b*T = 40*a*90*b
T=sqrt (40*90)= 60 mins
total time by A= 60+40 = 100 mins
let the time traveled by both a & b till meeting point is T mins
Let speed A = a, distance travelled by A in T mins = a*T
let speed B = b, distance travelled by B in T mins = b*T
after meeting point
A reached NY in 40 min at speed 'a':- distance = time * speed = 40*a
B reached Boston in 90 mins at speed 'b':- Distance = 90*b
distance travelled by A after meeting point = distance travelled by B before meeting point
therefore
b*T = 40*a.....................(1)
similarly a*T = 90*b.........(2)
multiply (1) and (2)
a*T * b*T = 40*a*90*b
T=sqrt (40*90)= 60 mins
total time by A= 60+40 = 100 mins
09 Mar 2022, 09:21
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Given: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met.
Asked: How long did Car A take to cover the distance between Boston and New York?
Let the speeds of car A & car B be vA & vB respectively and distance from New York to Boston be D.
At the time of meeting: -
Distance covered by car A = vA*D/(vA+vB)
Distance covered by car B = vB*D/(vA+vB)
Distance to be covered by car A = vB*D/(vA+vB)
Time taken by car A to cover the distance = (vB/vA)*D/(vA + vB) = 40 minutes
Distance to be covered by car A = vA*D/(vA+vB)
Time taken by car A to cover the distance = (vA/vB)*D/(vA + vB) = 90 minutes
(vB/vA)^2 = 40/90 = 4/9
vB/vA = 2/3
vA = 3(vA+vB)/5
vB = 2(vA+vB)/5
(vB/vA)*D/(vA + vB) = 40 = (2/5)(D/vA) = 40 minutes
D/vA = 40*5/2 = 100 minutes
Time taken by car A to cover the distance from New York to Boston = D/vA = 100 minutes = 1 hour 40 minutes
IMO D
Asked: How long did Car A take to cover the distance between Boston and New York?
Let the speeds of car A & car B be vA & vB respectively and distance from New York to Boston be D.
At the time of meeting: -
Distance covered by car A = vA*D/(vA+vB)
Distance covered by car B = vB*D/(vA+vB)
Distance to be covered by car A = vB*D/(vA+vB)
Time taken by car A to cover the distance = (vB/vA)*D/(vA + vB) = 40 minutes
Distance to be covered by car A = vA*D/(vA+vB)
Time taken by car A to cover the distance = (vA/vB)*D/(vA + vB) = 90 minutes
(vB/vA)^2 = 40/90 = 4/9
vB/vA = 2/3
vA = 3(vA+vB)/5
vB = 2(vA+vB)/5
(vB/vA)*D/(vA + vB) = 40 = (2/5)(D/vA) = 40 minutes
D/vA = 40*5/2 = 100 minutes
Time taken by car A to cover the distance from New York to Boston = D/vA = 100 minutes = 1 hour 40 minutes
IMO D
16 Aug 2022, 07:45
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Hey, looking at the answers provided, they are very helpful, but also quite technical. The approach I figured out to hack my way through the problem is:
1- We know they start at the same time and Car A then gets before to NY. So Car A is FASTER. This, in turn, implies the meeting point is closer to NY than to Boston.
2 - Since the meeting point is closer to NY, we have that 40min+40min<CAR A total journey< 40 min + 90 min. 1h20<CAR A total journey<2h10. This is the case since 2.1. The meeting point is further from Boston, so at least it took Car A 40 min to do Boston - Meeting Point & 2.2. Car A could not have taken longer than Car B to do Boston - Meeting Point.
ONLY possible answer is D. NO further computations required, just logic!
1- We know they start at the same time and Car A then gets before to NY. So Car A is FASTER. This, in turn, implies the meeting point is closer to NY than to Boston.
2 - Since the meeting point is closer to NY, we have that 40min+40min<CAR A total journey< 40 min + 90 min. 1h20<CAR A total journey<2h10. This is the case since 2.1. The meeting point is further from Boston, so at least it took Car A 40 min to do Boston - Meeting Point & 2.2. Car A could not have taken longer than Car B to do Boston - Meeting Point.
ONLY possible answer is D. NO further computations required, just logic!
Bluelagoon
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
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
