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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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woohoo921 wrote:
BrentGMATPrepNow wrote:
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'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)

Cheers,
Brent

BrentGMATPrepNow

Thank you for this helpful explanation. I would be so appreciative if you can correct me as to where I am making an error in setting up my rt=d chart below to solve this problem.

R * T = D
-----------------------------------------------
Ben: (20 mi/hr) (T +3) = D
Al: (40 mi/hr) T = D
------------------------------------------------
I wasn't sure what to set D equal to, but I know that the combined distance was 240 but just left each equation equal to D above. But, I am not sure where I went wrong based on what else I have.
=(60 mi/hr)*(2T+3)=240
--> t=1/2 is my answer based on how I set up my chart.

woohoo921

You asked Brent, but I notice what you're not doing, so I hope neither of you minds me chiming in.

You've set up an equation to find Ben's distance and an equation to find Al's distance. You called them both D, but they are not the same; you may have been more accurate to call them something like Dben and Dal. Anyway, the two distances combine to be 240 miles. So you have (20)(T+3)+(40)(T) = 240. From there, you get 20T+60+40T = 240. So 60T = 180, or T = 3. That's the amount of time Al drove. he started at 11am. 11am + 3 hours = 2pm. Make sense?
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
ThatDudeKnows
Thank you so much for your response! I truly appreciate it.

To clarify, what if they had different distances such as Ben's distance was 130 and Al's distance was 180. Would you add across the r*t=d chart like I did above to get (60 mi/hr)*(2T+3)=130+180 ? Or, would it still be (20)(T+3)+(40)(T) = 130 + 180.

In other words, I was confused as to how to order my operations for the r*t=d chart above when you combine the rates.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
woohoo921 wrote:
ThatDudeKnows
Thank you so much for your response! I truly appreciate it.

To clarify, what if they had different distances such as Ben's distance was 130 and Al's distance was 180. Would you add across the r*t=d chart like I did above to get (60 mi/hr)*(2T+3)=130+180 ? Or, would it still be (20)(T+3)+(40)(T) = 130 + 180.

In other words, I was confused as to how to order my operations for the r*t=d chart above when you combine the rates.

If you look back at the original question, we were actually never told that their distances were equal. They ended up being equal, but there was nothing until after we'd already answered the question that told us that! Your method was a-okay except that the two "D"s were not necessarily the same distance and you never added them together to get to 240.

Try tweaking the original question by changing "a combined total of 240 miles" to "a combined total of 180 miles" and see if you can derive (1) the time and (2) the distances that each driver traveled.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
Hi my friends,

I am back to this problem and was looking at it another way. I arrived at the correct answer. However, is my logic sound, or did I just stumble across the answer?

I decided to add the rates because Ben and Al are moving in opposite directions.

Step 1: I essentially put Ben and Al on equal footing by reducing the total distance by the amount that Ben would have driven before Al started driving --> 60 mi/hr * t =240-60
Step 2: I then solved to arrive at 3 hours, and then I added the 3 hours to 11 a.m., arriving at the answer of 2 p.m.

avigutman BrentGMATPrepNow

Thank you
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
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woohoo921 wrote:
Is my logic sound, or did I just stumble across the answer?

I decided to add the rates because Ben and Al are moving in opposite directions.

Step 1: I essentially put Ben and Al on equal footing by reducing the total distance by the amount that Ben would have driven before Al started driving --> 60 mi/hr * t =240-60
Step 2: I then solved to arrive at 3 hours, and then I added the 3 hours to 11 a.m., arriving at the answer of 2 p.m.

Yep nothing wrong with that, woohoo921.

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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
Here, since Ben and Al are moving in opposite directions, so their relative speeds will add up.

But time of start is not same in both cases.
At 11 am, Ben must have covered distance of 20 (m/h) * 3 h= 60 m.

Therfore, relative distance (after 11am) of both Ben and Al = 240-60= 180 m.

Now required time = 180/ (40+20) = 3 hours.

And 11am + 3hrs = 2 pm

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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
8 AM to 11 AM
Ben traveled 20 mph for 3 hours.
60 miles total
8 to 11 am.
Station ------------------------------->B
^60
From 11 am then it traveled the rest of the 240 - 60 = 180 distance.
11 am.
W<-----------------------------------------(AL)-Station---------------------------------------------->B
not yet started 60++

Relative distance: 20 + 40 = 60.
180/60 = 3 hours.

AL<--------------------------------------------Station--------------------------------------------------->B
40 + 40 + 40 = 120 (not counting the pre 60) + 20 + 20 + 20 = 60.

120 + 60 fits.

11 am to 2 pm.
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Re: Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]

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.

­We can also solve it by having Ben's time as a starting point (let's say it is t) and then Al's will be t + 3. Later on, as you said we use the equation A + B = 240 => 40*(t  + 3) = 20*t  and we will get immediately t = 2 so it's 2:00 p.m.

Let me know if it's correct the reasoning or is just a coincidence that I ended up to B .
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
time:                  8am 9am 10am 11am 12pm 13pm 14pm <----
BEN (20miles/h)    S     20     40     60      80    100    120
AI (40 miles/h)                              S       40      80    120

tot                                                        120   180    240 <---­
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Al and Ben are drivers for SD Trucking Company. One snowy day, Ben lef [#permalink]
Let x be the time when the measurment was made:

so Ben speed*hours droven by Ben + Al speed*hours droven by Al = 240 miles

then:

20(x-8) + 40(x-11) = 240

x=14

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