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29 Mar 2018, 00:42
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
92% (01:36) correct
8%
(02:09)
wrong
based on 136
sessions
History
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Time
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Two vehicles leave the same location at the same time. The first vehicle travels due east at 70 miles per hour. The other vehicle travels due west at 60 miles per hour. Assuming they continue at their respective speeds without stopping, how long (in hours) will it take for the two vehicles to be 455 miles apart?
(A) 2.75
(B) 3.5
(C) 4.25
(D) 4.75
(E) 5.5
(A) 2.75
(B) 3.5
(C) 4.25
(D) 4.75
(E) 5.5
29 Mar 2018, 01:16
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Bunuel
The vehicles are moving opposite to each other, hence speed with which distance between them increases is 70 + 60 mph
d = speed * time
\(455 = 130 * t\)
\(t = 455 /130\)
\(t = 3.5\)
Hence Option (B) is correct.
Best,
Gladi
29 Mar 2018, 03:48
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Bunuel
The best method to answer this question will be using the Relative speed
Relative speed of the two objects is defined as change ijn distance between the two objects in unit time
i.e. Relative speed of two moving objects with speed a and b travelling in same direction = a-b
and Relative speed of two moving objects with speed a and b travelling in Opposite direction = a+b
The the case given to us is the case of two trains moving in opposite directions hence
Relative Speed = 70+60 = 130 miles per hour
Time = Relative Distance / Relative Speed
i.e. Time = 455 / 130 = 3.5 Hours
Answer: option B
ALTERNATIVE:
Let, After t hours the distance between the two trains = 455 miles
Distance travelled by First train in t hours = Speed * Time = 70*t
Distance travelled by Second train in t hours = Speed * Time = 60*t
Total Distance travelled by the two trains together = 70t + 60t = 455 (Given)
i.e. 130t = 455
i.e. t = 3.5
Answer: option B
