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Ashu9876
Joined: 05 Sep 2022
Last visit: 01 Dec 2023
Posts: 12
Own Kudos:
Given Kudos: 1
Location: India
Schools: Wharton '25
21 Mar 2023, 23:37
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Sol.
Given: Speed of Train A – 100mph
Start time for A from New York – 3PM
Start time for B from Boston – 3:50PM
Meeting time for A and B – 4PM
Total travel time is 2 Hour
Need: Speed of train B, Distance from New York to Boston
Assume distance is d miles and speed of Train B is x mph
d = 100*1 + (10/60) x , d – 100 = x/6
Basically we are looking for the value of x.
Then,
After 1 hour of A, time taken by A to reach Boston + time taken by B to reach New York = 50 minutes.
(x/6)/100 +100/x=50/60 , x/600 +100/x=50/60
x^2-500x +60000=0
Solving above, x = 200 and 300
Statement (1): Train B arrived in New York before Train A arrived in Boston
x/600>100/x,x>100√6
x>100*2.44 ,x>244
Hence x = 300 and St1 is sufficient
BCE eliminated, Remaining AD
Statement (2): The distance between New York and Boston is greater than 140 miles.
d>140,100+x/6>140,x>240
then x=300
Answer choice A eliminated, Hence D is the answer.
Given: Speed of Train A – 100mph
Start time for A from New York – 3PM
Start time for B from Boston – 3:50PM
Meeting time for A and B – 4PM
Total travel time is 2 Hour
Need: Speed of train B, Distance from New York to Boston
Assume distance is d miles and speed of Train B is x mph
d = 100*1 + (10/60) x , d – 100 = x/6
Basically we are looking for the value of x.
Then,
After 1 hour of A, time taken by A to reach Boston + time taken by B to reach New York = 50 minutes.
(x/6)/100 +100/x=50/60 , x/600 +100/x=50/60
x^2-500x +60000=0
Solving above, x = 200 and 300
Statement (1): Train B arrived in New York before Train A arrived in Boston
x/600>100/x,x>100√6
x>100*2.44 ,x>244
Hence x = 300 and St1 is sufficient
BCE eliminated, Remaining AD
Statement (2): The distance between New York and Boston is greater than 140 miles.
d>140,100+x/6>140,x>240
then x=300
Answer choice A eliminated, Hence D is the answer.
11 Mar 2024, 08:07
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Why can't we assume time to be (T+5/6) for train A? Train A leaves 50 minutes earlier than train B.
I made the equation 2T+5/6=2 hours. Can anyone tell me why this approach doesn't work in this question ?
I made the equation 2T+5/6=2 hours. Can anyone tell me why this approach doesn't work in this question ?
11 Mar 2024, 21:37
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aj2348
You are assuming that time taken by train B for the journey is T and hence by train A is T+5/6 (because it started 50 mins earlier). But we are not given that both trains reach their destinations at the same time. In fact, statement 1 tells us that they don't.
