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A car traveled 75 percent of the distance from town A to town B by tra

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A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 02 Nov 2017, 23:24
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A car traveled 75 percent of the distance from town A to town B by traveling for T hours at an average speed of V miles per hour. The car traveled at an average speed of S miles per hour for the remaining part of the trip. Which of the following expressions represents the time the car traveled at S miles per hour?

(A) VT/S
(B) VS/(4T)
(C) 4VT/(3S)
(D) 3S/(VT)
(E) VT/(3S)

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Re: A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 02 Nov 2017, 23:38
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Bunuel wrote:
A car traveled 75 percent of the distance from town A to town B by traveling for T hours at an average speed of V miles per hour. The car traveled at an average speed of S miles per hour for the remaining part of the trip. Which of the following expressions represents the time the car traveled at S miles per hour?

(A) VT/S
(B) VS/(4T)
(C) 4VT/(3S)
(D) 3S/(VT)
(E) VT/(3S)


Case 1: S = V miles/Hr; T = T hrs; D = VT
Case 2: S = S miles/Hr; T = x hrs; D = xS

VT:xS::3:1
x = VT/3S

E
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Re: A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 03 Nov 2017, 03:01
RTD chart, let x be the distance and y time to cover the remaining distance with V speed:
R T D
Vm/h Th. 0,75x
Sm/h yh. 0,25x

To make the correct equation we should to find x in terms of (VT) and in terms of (Sy)
0,75x=VT ==> x=VT/0,75
0,25x=Sy ==> x=Sy/0,25

VT/0,75=Sy/0,25
solving
y=VT/3S

Answer E.
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A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 04 Nov 2017, 16:17
1
Bunuel wrote:
A car traveled 75 percent of the distance from town A to town B by traveling for T hours at an average speed of V miles per hour. The car traveled at an average speed of S miles per hour for the remaining part of the trip. Which of the following expressions represents the time the car traveled at S miles per hour?

(A) VT/S
(B) VS/(4T)
(C) 4VT/(3S)
(D) 3S/(VT)
(E) VT/(3S)

Choose smart numbers.
For \(\frac{3}{4}\), I kept the ratio but increased the values slightly to \(\frac{6}{8}\)
Let distance for leg 1 = 6
Let distance for leg 2 = 2

Let V = leg 1 speed = 3 mph, hence
T = leg 1 time = \(\frac{6}{3}=\) 2 hrs
Let S = leg 2 speed = 1, hence
?? = leg 2 time = \(\frac{2}{1}=\) 2 hrs

With T = 2, V = 3, S = 1, find the answer choice that yields 2

(A) VT/S: 6/1 = 6. No match

(B) VS/(4T): 3/2. No match

(C) 4VT/(3S):24/3 = 8. No match.

(D) 3S/(VT): 3/6 = 1/2. No match.

(E) VT/(3S): 6/3 = 2. MATCH

Answer E
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Re: A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 06 Nov 2017, 17:37
Bunuel wrote:
A car traveled 75 percent of the distance from town A to town B by traveling for T hours at an average speed of V miles per hour. The car traveled at an average speed of S miles per hour for the remaining part of the trip. Which of the following expressions represents the time the car traveled at S miles per hour?

(A) VT/S
(B) VS/(4T)
(C) 4VT/(3S)
(D) 3S/(VT)
(E) VT/(3S)


If we let d = the total distance, then during the first part of the trip, we have:

VT = 0.75d

VT/0.75 = d

VT/(3/4) = d

4VT/3 = d

So, the remaining distance is:

0.25(4VT/3) = VT/3

Since the car traveled at S miles per hour, the time was (VT/3)/S = VT/(3S).

Answer: E
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Re: A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 10 Jun 2018, 23:02
Bunuel wrote:
A car traveled 75 percent of the distance from town A to town B by traveling for T hours at an average speed of V miles per hour. The car traveled at an average speed of S miles per hour for the remaining part of the trip. Which of the following expressions represents the time the car traveled at S miles per hour?

(A) VT/S
(B) VS/(4T)
(C) 4VT/(3S)
(D) 3S/(VT)
(E) VT/(3S)



According to the question,

V x T = 75% x D
or D = (V x T)/75% ....(1)

S x T2 = 25% x D
or D = (S x T2)/25% ....(2)

Now, combining (1) & (2) we get

VT/75% = ST2/25%

or T2 = VT/75% x 25%/S

or T2 = VT/3S

Answer is (E)

KUDOS if it helped!
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Re: A car traveled 75 percent of the distance from town A to town B by tra  [#permalink]

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New post 11 Jun 2018, 00:17
From above information, 3/4 of AB = VT ==> AB = VxT/3.

Call the time the car traveled at S miles per hour is T'. We have equation: 1/4 of AB = T'xS ==> S = 1/4xAB/S = VxT/3S ==> Answer E
Re: A car traveled 75 percent of the distance from town A to town B by tra &nbs [#permalink] 11 Jun 2018, 00:17
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