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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef

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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 17 Jun 2017, 08:29
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

A. 1:00 p.m.
B. 2:00 p.m.
C. 3:00 p.m.
D. 5:00 p.m.
E. 6:00 p.m.

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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 26 Sep 2017, 15:41
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AbdurRakib wrote:
Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

A. 1:00 p.m.
B. 2:00 p.m.
C. 3:00 p.m.
D. 5:00 p.m.
E. 6:00 p.m.


Let t represent the time passed between the departure of Al (11:00 a.m.) and the retrieval of data by the dispatcher. Since Ben left at 8 a.m., his time is (t + 3). Since they both traveled for a total 240 miles, we can use the formula distance = rate x time and create the following equation:

Ben’s distance + Al’s distance = 240

20(t + 3) + 40t = 240

20t + 60 + 40t = 240

60t = 180

t = 3 hours

Thus, it was 11 a.m. + 3 hours = 2 p.m. when the dispatcher retrieved data from the vehicle tracking system.

Answer: B
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 17 Jun 2017, 08:47
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AbdurRakib wrote:
Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

A. 1:00 p.m.
B. 2:00 p.m.
C. 3:00 p.m.
D. 5:00 p.m.
E. 6:00 p.m.


Ben started at 8 am and given his avg speed is 20 miles per hour.

Al started at 11 am and given his avg speed is 40 miles per hour.

Ben started 3 hours earlier than Al.

Therefore distance covered by Ben in 3 hours = 20 x 3 = 60 miles

Given Total distance covered by both Ben and Al = 240 miles.

Distance covered by Ben and Al after Al started his journey at 11 am = 240 - 60 = 180 miles.

Relative speed = 20 + 40 = 60 miles per hour --------- (Ben and Al are driving in opposite directions hence their speeds are added)

Time = Total distance / Relative speed

Time = \(\frac{180}{60}\) = 3 hours.

Time when dispatcher retrieved data = 11:00 am + 3 hours = 2:00 pm. Answer (B)...
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 17 Jun 2017, 08:44
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AbdurRakib wrote:
Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

A. 1:00 p.m.
B. 2:00 p.m.
C. 3:00 p.m.
D. 5:00 p.m.
E. 6:00 p.m.


3 hours+(240-3*20)/(40+20) hours=6 hours
2:00 pm
B
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post Updated on: 17 Apr 2018, 06:59
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AbdurRakib wrote:
Al and Ben are drivers for SD Trucking Company. One snowy day, Ben left SD at 8:00 a.m. heading east and Al left SD at 11:00 a.m. heading west. At a particular time later that day, the dispatcher retrieved data from SD’s vehicle tracking system. The data showed that, up to that time, Al had averaged 40 miles per hour and Ben had averaged 20 miles per hour. It also showed that Al and Ben had driven a combined total of 240 miles. At what time did the dispatcher retrieve data from the vehicle tracking system?

A. 1:00 p.m.
B. 2:00 p.m.
C. 3:00 p.m.
D. 5:00 p.m.
E. 6:00 p.m.


Let's start with a "word equation"

(Ben's travel distance) + (Al's travel distance) = 240 miles

Let t = Al's travel time (in hours)
So, t + 3= Ben's travel time (since Ben spent 3 more hours driving)

Distance = (rate)(time)

So, our word equation becomes...
(20)(t + 3) = (40)(t)
Expand: 20t + 60 = 40t
Subtract 20t from both sides: 60 = 20t
Solve: t = 3
So, AL traveled for 3 hours (which means BEN traveled for 6 hours)

So, the dispatcher retrieved data at 2pm (since 8am + 6 hours = 2pm)

Answer: B

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Originally posted by GMATPrepNow on 28 Jun 2017, 06:14.
Last edited by GMATPrepNow on 17 Apr 2018, 06:59, edited 2 times in total.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 02 Jul 2017, 20:28
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Both are going in opposite directions. In 3 hours, Ben has already covered = 20*3 = 60 miles.

Now, at 11 am, both have started moving, Al covering 40 miles in 1 hour while Ben covering 20 miles per hour, so from 11 am onwards, both are now increasing the distance between them by (40+20) = 60 miles every hour.

So out of the given 240 miles distance between them, 60 miles is accounted for by Ben from 8 to 11 am. After that they have covered (240-60) = 180 miles, but their relative speed is 60 mph. So time taken = 180/60 = 3 hours more, after 11 am

So the time must be 2.00 pm. Hence B answer
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 03 Jul 2017, 09:40
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Lets say Ben drove "y" hours and Al drove "x" hours
We know that the sum of both they're hours took them to drive 240 miles
40x+20y= 240
And we know that Al left 3 hours after Ben
y=x+3
So we just replace y in the first equation
40x+20(x+3)=240
40x+20x+60=240
60x=180
x=3

Since AL left at 11, then 11+3 means the dispatcher retrieved the data at 2pm or 14.00
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 01 Sep 2017, 23:32
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The answer is 'B' - 2:00PM. I will only try to explain this problem practically:

Time taken to travel ---> 8am - 9am - 10am - 11am - 12am - 1pm - 2 pm
Al (distance covered @20km/h 20km 40 60 . 80 . 100 . 120 ----
Ben (distance covered @40km/h) . - - - 0 . 40kms 80 . 120


Total distance covered 240kmph by both after 1pm, thus 2PM is answer.
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post Updated on: 24 Sep 2017, 02:08
sashiim20 Bunuel Engr2012
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Quote:
Distance covered by Ben and Al after Al started his journey at 11 am = 240 - 60 = 180 miles.


Has not Al just started journey at 11 am? At 11 am distance traveled by Al shall be zero

Also as per Q after a particular time the data is logged, so above quote seems not to be inferred at 11 am.
Am I correct?

Originally posted by adkikani on 22 Sep 2017, 22:38.
Last edited by adkikani on 24 Sep 2017, 02:08, edited 1 time in total.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 24 Sep 2017, 01:56
B.) is the answer

Rate B = 20mph
Rate A = 40mph

20x+40y= 240miles

x=6 & y=3

Ben= 8:00+6= 14:00
Al= 11:00+3= 14:00

14:00-12:00= 2pm
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 02 Oct 2017, 23:50
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Total Distance covered by al + ben =240 km

Ben left at 8:00 am at 20miles/ hr

Al left at 11:00 am at 40/ miles hr

So by logic 240 = 20 + 20 + 20 ( distance covered in 3 hours by ben) + 60 + 60 +60 ( Total distance covered by ben and al)
= 6 hrs

Therefore 8:00 am + 6 hrs = 2:00 pm

This is how I calculated.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 02 Nov 2017, 16:21
adkikani wrote:
sashiim20 Bunuel Engr2012
VeritasPrepKarishma

Quote:
Distance covered by Ben and Al after Al started his journey at 11 am = 240 - 60 = 180 miles.


Has not Al just started journey at 11 am? At 11 am distance traveled by Al shall be zero

Also as per Q after a particular time the data is logged, so above quote seems not to be inferred at 11 am.
Am I correct?


Has not Al just started journey at 11 am? At 11 am distance traveled by Al shall be zero - That's correct. At 11 am Al has covered a distance of 0 miles.

Also as per Q after a particular time the data is logged, so above quote seems not to be inferred at 11 am. - The quote that you are referring to is for time 11 am. The reason it is first calculated till 11 is because only Ben's speed is considered first (So at 11 am the total distance traveled by Ben + Al = 60 miles). From 11 am we have both Ben's + Al's speed. The Q is asking for the time when the total distance covered (Ben + Al = 240 miles) and that is 2 pm.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 07 Dec 2017, 13:41
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Hi All,

This prompt gives us a lot of different facts about rates, times and distances, so we're clearly going to use the distance formula here:

Distance = (Rate)(Time)

We're looking for the time at which the distance between the two drivers was 240 miles - and since the answer choices are 5 times, we can use them 'against' the prompt and TEST THE ANSWERS.

Let's Test Answer B: 2:00pm
At 2pm....
Ben would have been driving for 6 hours at 20 miles/hour = 120 miles driven
Al would have been driving for 3 hours at 40 miles/hour = 120 miles driven
Total Distance = 120 miles + 120 miles = 240 miles
This is an exact MATCH for what we were told, so this MUST be the answer!

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Re: AI & BEN are drivers for SD Trucking company. one snowy day, Ben left  [#permalink]

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New post 28 May 2018, 21:35
viveknegi wrote:
AI & BEN are drivers for SD Trucking company. one snowy day, Ben left SD at 8:00 am, heading east
and AI left SD at 11:00 am, heading west. At a particular time later that day, the dispatcher retrieved
data from SD's vehicle tracking system. The data showed that, up to that time, AI had averaged 40mph
and Ben had averaged 20mph. It also showed that AI and Ben had driven a combined total of 240 miles.
At what time did the dispatcher retrieve data from the vehicle tracking system?

A) 1:00 pm
B) 2:00 pm
C) 3:00 om
D) 5:00 pm
E) 6:00 pm


The vehicle tracking system gave us the following details
AI's average speed - 40 mph
Ben's average speed - 20 mph
Combined distance traveled - 240 miles

Since AI started at 11 am, Ben would have already traveled alone for 3 hours.
In 3 hours, traveling at 20 mph, he would have traveled 60 miles. Once, Ben
joins him, together they would have traveled 60 miles.

\(60 + 60x = 240\) -> \(60x = 180\) -> \(x = \frac{180}{60} = 3\)

Therefore, the time at which the dispatcher retrieved the data was at 2:00 PM(Option B), 3 hours after 11 AM, when AI left SD.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 28 Aug 2018, 03:19
Please tell me where i am wrong.

Al distance covered till 11 a.m at avg speed of 40m/hr is 120 miles. Remaining distance is 240-120 = 120 miles.
The combined average speed will be 60 miles/hr and after 11 a.m the time taken to cover 120 miles will be 2 hours.
Total time taken is 5 hours which will be 8 a/m + 5 hours = 13.00 hrs. i,e 1 p.m.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 28 Aug 2018, 15:33
brains wrote:
Please tell me where i am wrong.

Al distance covered till 11 a.m at avg speed of 40m/hr is 120 miles. Remaining distance is 240-120 = 120 miles.
The combined average speed will be 60 miles/hr and after 11 a.m the time taken to cover 120 miles will be 2 hours.
Total time taken is 5 hours which will be 8 a/m + 5 hours = 13.00 hrs. i,e 1 p.m.


Hi brains! Your reasoning is good; you just used Al's speed instead of Ben's speed for the first 3 hours. If you use Ben's speed of 20 miles/hour for the first 3 hours, he covers 60 miles, leaving 180 miles for the remaining time. That distance is covered at 60 miles/hour, so the time taken is 3 more hours after 11am. That is how we get to 2pm instead of 1pm.

Please let me know if you have any questions about that!
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef  [#permalink]

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New post 29 Aug 2018, 18:19
There are already excellent solutions for this question in this thread, but I thought I would offer up an alternative solution for those who may prefer to work with numbers rather than algebra. This involves using a table to organize the information, which some people may find faster and less confusing than setting up an algebraic equation. Here are the specific GMAT Timing Tips that I suggest for this question (the links have growing lists of questions that you can use to practice each tip):

Use D = R x T and W = R x T on rate problems: Like nearly every distance rate and work rate problem, this question will probably go more quickly if you remember to use the appropriate rate equation, in this case D = R x T (Distance = Rate x Time).

Use relative rates when two objects are moving: Notice that Al and Ben are moving in opposite directions, so their relative rate of motion — the rate at which the distance is changing between them — is the sum of their rates: 20 miles/hour + 40 miles/hour = 60 miles/hour. We can also think of this as the rate at which they collectively cover distance while they are both moving.

Use tables to organize rate problems with multiple scenarios: While it is possible to go straight to writing an equation to solve this problem, some may find it faster and less confusing to organize the information for this problem in a table. The columns of the table are Distance, Rate, and Time, remembering that Distance = Rate x Time. Each row of the table represents one of the two scenarios in this question: The first row represents the period 8-11am when only Ben is driving, and the second row represents the period after 11am when both Al and Ben are driving. The table that I created for this problem is shown below. Note that I filled in the boxes in the table in this order:
1) The total distance (below the table) is 240 miles, so the distances in the two rows above must add up to 240 miles.
2) The time for 8-11am is 3 hours.
3) The rate for 8-11am is 20 miles/hour (Ben’s speed).
4) Because Distance = Rate x Time, the distance for 8-11am is 60 miles.
5) Because the total distance must be 240 miles, the distance for 11am-? must be 240 – 60 = 180 miles.
6) The rate for 11am-? is 20 + 40 = 60 miles/hour (the sum of Al’s and Ben’s speeds).
7) Because Distance = Rate x Time, the time for 11am-? is (180 miles) / (60 miles/hour) = 3 hours. Thus, the answer is 3 hours after 11am, or 2:00 p.m.

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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef &nbs [#permalink] 29 Aug 2018, 18:19
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