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Two vehicles leave the same location at the same time. The first vehic

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Two vehicles leave the same location at the same time. The first vehic  [#permalink]

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New post 29 Mar 2018, 00:42
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Question Stats:

87% (01:39) correct 13% (02:24) wrong based on 86 sessions

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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

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Re: Two vehicles leave the same location at the same time. The first vehic  [#permalink]

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New post 29 Mar 2018, 01:16
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Bunuel wrote:
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


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.

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Two vehicles leave the same location at the same time. The first vehic  [#permalink]

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New post 29 Mar 2018, 03:48
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Bunuel wrote:
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


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
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Re: Two vehicles leave the same location at the same time. The first vehic  [#permalink]

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New post 30 Mar 2018, 10:51
Bunuel wrote:
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


We can let t = the time each car drives and create the equation:

70t + 60t = 455

130t = 455

t = 455/130 = 3.5 hours

Answer: B
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Re: Two vehicles leave the same location at the same time. The first vehic  [#permalink]

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New post 14 Apr 2018, 23:18
Bunuel wrote:
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


Effective speed = 60 + 70 = 130 m/h

Distance = 455 m

Therefore, Effective time = \(\frac{455}{130}\)= \(\frac{7}{2}\)= \(3.5 hrs\)

(B)
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Re: Two vehicles leave the same location at the same time. The first vehic   [#permalink] 14 Apr 2018, 23:18
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