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

Question

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.

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.

JeffTargetTestPrep · Accepted Answer

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

sashiim20 · Answer

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)...

BrentGMATPrepNow · Answer

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 ) = 240 miles
Expand: 20t + 60 + 40t = 240
Simplify: 60t + 60 = 240
Subtract 60 from both sides: 60t = 180
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

Cheers,
Brent

gracie · Answer

3 hours+(240-3*20)/(40+20) hours=6 hours
2:00 pm
B

amanvermagmat · Answer

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

Sofiv7 · Answer

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

AnubhavK · Answer

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.

EMPOWERgmatRichC · Answer

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!

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

brains · Answer

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.

JeffYin · Answer

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!

JeffYin · Answer

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.

https://yintutoring.com/wp-content/uploads/2018/08/OG2019-082-diagram.png

Please let me know if you have any questions, or if you would like me to post a solution video!

badly777 · Answer

Why equation 40(t-3)+20t=240 is not working, can you explain, please?

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=k5B27b-dfUM

kvsahi08 · Answer

I am not so good with forming equations so I solved it without adding any variables to the solution and here is how it ended up.

Ben started 3hrs before al so, by 11am, Ben travelled =3hrs*20mph(his average speed)=60 miles. 
=> Remaining total distance falls to 240-60= 180miles.
According to the difference in average speed of Ben and al 40-20 miles respectively, al is 2 times faster than Ben 
=> al travelled twice that of Ben of total distance 
=> al=60 and Ben=120 
For Ben or al to travel their respective miles it would take 20mph*3hrs = 60 or 40mph*3hrs = 120, respectively.

There fore the data is taken after 3 hrs of 11am. => 2pm

CEdward · Answer

Hi guys, Why are we adding the 3 hours to 11 pm rather than 8? I know adding to 8 to get 11 is not an option, but just want to understand clearly why that is? (There are other styles of question where this is important).

EMPOWERgmatRichC · Answer

Hi CEdward,

Since Ben began driving at 8:00am, he was driving for 3 hours BEFORE Al even started driving. Once you have accounted for that "alone time" - which brings us up to 11:00am - then both men were driving. Depending on how you approached the calculations involved, you will eventually determine that they BOTH had to have been driving for 3 hours (from 11:00am to 2:00pm) to hit the overall 240 miles in total distance traveled. 
 
GMAT assassins aren't born, they're made,
Rich

BLTN · Answer

Dear  badly777 
you solution is utterly right
Mere take into consideration that 40km is Al's speed and he started 3 after Ben, that is t-3
Hence, in you case "t" is Ben time = 8 am.

40(t-3)+20t=240
40t - 120 + 20t = 240
60t = 240 +120
t = 6 hours

Ben time: t = 8 am + 6 hours = 14 pm.

Hope it helps.

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=EpQpgQPJIP4

ThatDudeKnows · Answer

As soon as I consider setting up an algebraic equation, I think about whether Plugging In The Answers (PITA) is a good option. I like trying B and D.

Let's start with B.
If Ben drives from 8am-2pm, that's 6 hours. At 20mph, that's 120 miles.
Al drives from 11am-2pm, so that's 3 hours. At 40mph, that's 120 miles.
Add them together and we get 240 miles, which is what we wanted.

Answer choice B

ThatDudeKnowsPITA

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

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My Rewards