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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?

Re: Robert drives from City A to City B [#permalink]

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31 Mar 2011, 06:43

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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

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

Re: Robert drives from City A to City B [#permalink]

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31 Mar 2011, 07:26

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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: Robert drives from City A to City B [#permalink]

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07 Aug 2013, 11:14

Hi Bunnel Please help me out to check the my approach

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

Re: Robert drives from City A to City B [#permalink]

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07 Aug 2013, 12:35

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:

Re: Robert drives from City A to City B [#permalink]

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08 Aug 2013, 00:44

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: Robert drives from City A to City B [#permalink]

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27 May 2014, 14:43

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 .

Re: Robert drives from City A to City B [#permalink]

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28 May 2014, 15:42

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"

Re: Robert drives from City A to City B [#permalink]

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