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

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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.

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

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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

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

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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)...

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)

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

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02 Jul 2017, 20:28

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

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

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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

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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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.

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!