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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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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.
[Reveal] Spoiler: OA

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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, 09:44
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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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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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]

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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:
[Reveal] Spoiler:
B


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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, 21:28
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

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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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 02 Sep 2017, 00:32
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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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef   [#permalink] 02 Sep 2017, 00:32
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