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# Yesterday it took Robert 3 hours to drive from City A to City B. Today

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Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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31 Mar 2011, 05:11
1
5
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:54) correct 33% (02:13) wrong based on 306 sessions

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Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

(A) 90
(B) 120
(C) 150
(D) 240
(E) 300

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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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31 Mar 2011, 05:43
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2
Pkit wrote:
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

(A) 90
(B) 120
(C) 150
(D) 240
(E) 300

15 minutes less in each trip.

A to B, Actual time=3 hours; If 15 minutes saved, 2hours 45minutes i.e. t=2.75hours
B to A, Actual time=2 hours 30 minutes; If 15 minutes saved, 2hours 15 minutes i.e. t=2.25hours

$$Average \hspace{1} speed = \frac{Total \hspace{1} Distance}{Total \hspace{1} Time}$$

Let the distance between A and B be D.
$$Average \hspace{1} speed = \frac{D+D}{2.75+2.25}$$
$$60 = \frac{2D}{5}$$
$$D = \frac{60*5}{2} = 150 \hspace{1} miles$$

Ans: "C"
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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31 Mar 2011, 05:33
2
2d/60 = 5 ( because time = 3 + 2.5 - 0.5 hrs)

=> d = 150

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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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31 Mar 2011, 06:26
1
15+15=30min or 0.5 hrs =saving time in both trips
d= distance between A and B
distance=speed*time
2*d=speed * (total time=3+2.5-0.5=5) ==> d=(60*5)/2 ==>d=150
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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31 Mar 2011, 06:33
guys
thank you a lot ,
you are the math gurus ))
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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07 Aug 2013, 10:14
Hi Bunnel

Lets say total distance for round trip is 2D and given that speed is 60 miles per hours for round trip as well.
R*T=D now 60*T=2D again T is total time taken for round trip.

So the equation would be T=2D/30 and T=time taken for round trip now total time is 2.5+3=5.5

So 5.5=2D/30 =>55/10=2D/30 =>D=150 ans......

Rgds
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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07 Aug 2013, 11:35
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

Total round trip time = 5.5 hours (330 minutes)
t=330
speed = distance/time
60 = 2d/t-2*(15)
60 = 2d/t-30
60t-1800 = 2d
30t - 900 = d

I messed up here two ways. First, I converted hours to minutes. After realizing this was a mistake, I plugged in the total number of hours (5) for t but still subtracted 30 minutes from t when I should have converted subtracted the fraction that 15 minutes takes off of each trip from the total time.

(subtracting 15 minutes from both trips)
AB - 2.75 hours
BA - 2.25 hours

Speed = distance/time
we are given the average speed if 15 minutes were shaved off of each leg of the trip and the time for each leg of the trip. With this information we can solve for d.

60 = 2d/(2.75 + 2.25)
60 = 2d/5
300 = 2d
150 = d

An alternative way of solving using d=r*t formula:

2d=s*t
2d=60*(2.75+2.25)
2d=60*(5)
2d=300
d=150
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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07 Aug 2013, 23:44
1
PTK wrote:
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

(A) 90
(B) 120
(C) 150
(D) 240
(E) 300

solution: S = Vt
2AB = 60 {(3-15/60)+(5/2 - 15/60)}
or, AB = 150 (Answer C)

But question needs a correction.
If he had saved 15 minutes in both trips it should be if he had saved 15minutes in each of his trip .
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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27 May 2014, 13:43
Asifpirlo wrote:
PTK wrote:
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

(A) 90
(B) 120
(C) 150
(D) 240
(E) 300

solution: S = Vt
2AB = 60 {(3-15/60)+(5/2 - 15/60)}
or, AB = 150 (Answer C)

But question needs a correction.
If he had saved 15 minutes in both trips it should be if he had saved 15minutes in each of his trip .

Agree with this, wording is ambiguous.

Bunuel could you confirm this?

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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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27 May 2014, 22:50
Let the distance between both cities = d

Time taken from City A to City B = 180 Mins
Time taken from City B to City A = 150 Mins

If saved 15 mins in both trips each, Avg speed of round trip = 60 Miles per hr = 1 Mile per min

Setting up the equation

$$(180 - 15) + (150 - 15) = \frac{d + d}{1}$$

d = 150

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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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28 May 2014, 14:42
1
i find that the phrasing of the question is wrong, regardless the fact that it is an easy question.
" he saved 15 min in both trips" should be "he saved 15 min in each trip"
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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today  [#permalink]

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03 Aug 2018, 14:11
PTK wrote:
Yesterday it took Robert 3 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 60 miles per hour. What is the distance between city A and city B?

(A) 90
(B) 120
(C) 150
(D) 240
(E) 300

If he saved 15 minutes, or 0.25 hours, in each leg of the round trip, the total number of hours spent driving would be (3 - 0.25) + (2.5 - 0.25) = 2.75 + 2.25 = 5 hours. Since the speed would then be 60 miles per hour, the round-trip distance must be 5 x 60 = 300 miles, and thus the one-way distance (i.e., distance between city A and city B) is 150 miles.

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Re: Yesterday it took Robert 3 hours to drive from City A to City B. Today &nbs [#permalink] 03 Aug 2018, 14:11
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