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Rate problem - Time taken for trains

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Rate problem - Time taken for trains

by gmattesttaker2 » Sat Oct 26, 2013 5:33 pm
Hello,

Can you please assist with this?

Train A leaves New Orleans and travels at a rate of 60 mph; an hour later, a second train
leaves from the same station and along the same track travelling at a rate of 80 mph. How long will it
take, from its departure point, for the second train to be 60 miles ahead of the first one?

OA : 2

My approach was as follows:

Rate x Time = Distance

A: 60 x t = 60t
B: 80 X (t-1) = 80(t - 1)

So, 80(t-1) = 60t + 60
=> 80t - 80 = 60t + 60
=> 20t = 140
=> t = 7 hrs

Can you please tell me where I am going wrong? Thanks for your help.
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by Uva@90 » Sat Oct 26, 2013 6:48 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this?

Train A leaves New Orleans and travels at a rate of 60 mph; an hour later, a second train
leaves from the same station and along the same track travelling at a rate of 80 mph. How long will it
take, from its departure point, for the second train to be 60 miles ahead of the first one?

OA : 2

My approach was as follows:

Rate x Time = Distance

A: 60 x t = 60t
B: 80 X (t-1) = 80(t - 1)

So, 80(t-1) = 60t + 60
=> 80t - 80 = 60t + 60
=> 20t = 140
=> t = 7 hrs

Can you please tell me where I am going wrong? Thanks for your help.
Hi Gmattesttaker2,
Are you sure OA is 2 ?

You can also cross check,
At 0 Hours for Train B,
Train A would have already covered 60 Miles
Train B would have covered 0 Miles

At 1 Hours for Train B,
Train A would have already covered 120 Miles(60+60)
Train B would have already covered 80 Miles

At 2 Hours for Train B,
Train A would have already covered 180 Miles(60+60+60)
Train B would have already covered 160 Miles(80+80)

At 3 Hours for Train B,
Train A would have already covered 240 Miles(60+60+60+60)
Train B would have already covered 240 Miles(80+80+80)

At 4 Hours for Train B,
Train A would have already covered 300 Miles(60+60+60+60+60)
Train B would have already covered 320 Miles(80+80+80+80)
Now the distance between them is 320-300 = 20 miles

At 5 Hours for Train B,
Train A would have already covered 360 Miles(60+60+60+60+60+60)
Train B would have already covered 400 Miles(80+80+80+80+80)
Now the distance between them is 400-360 = 40 miles

At 6 Hours for Train B,
Train A would have already covered 420 Miles(60+60+60+60+60+60+60)
Train B would have already covered 480 Miles(80+80+80+80+80+80)
Now the distance between them is 480-420 = 60 miles

So 6 hours after its departure point Train B will be 60 miles ahead of Train A.

In your Solution,
You have solved the time for the train A,
But in Question they have asked the time for Train B
hence 7-1 = 6

Regards,
Uva.
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by gmattesttaker2 » Sat Oct 26, 2013 9:40 pm
Uva@90 wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this?

Train A leaves New Orleans and travels at a rate of 60 mph; an hour later, a second train
leaves from the same station and along the same track travelling at a rate of 80 mph. How long will it
take, from its departure point, for the second train to be 60 miles ahead of the first one?

OA : 2

My approach was as follows:

Rate x Time = Distance

A: 60 x t = 60t
B: 80 X (t-1) = 80(t - 1)

So, 80(t-1) = 60t + 60
=> 80t - 80 = 60t + 60
=> 20t = 140
=> t = 7 hrs

Can you please tell me where I am going wrong? Thanks for your help.
Hi Gmattesttaker2,
Are you sure OA is 2 ?

You can also cross check,
At 0 Hours for Train B,
Train A would have already covered 60 Miles
Train B would have covered 0 Miles

At 1 Hours for Train B,
Train A would have already covered 120 Miles(60+60)
Train B would have already covered 80 Miles

At 2 Hours for Train B,
Train A would have already covered 180 Miles(60+60+60)
Train B would have already covered 160 Miles(80+80)

At 3 Hours for Train B,
Train A would have already covered 240 Miles(60+60+60+60)
Train B would have already covered 240 Miles(80+80+80)

At 4 Hours for Train B,
Train A would have already covered 300 Miles(60+60+60+60+60)
Train B would have already covered 320 Miles(80+80+80+80)
Now the distance between them is 320-300 = 20 miles

At 5 Hours for Train B,
Train A would have already covered 360 Miles(60+60+60+60+60+60)
Train B would have already covered 400 Miles(80+80+80+80+80)
Now the distance between them is 400-360 = 40 miles

At 6 Hours for Train B,
Train A would have already covered 420 Miles(60+60+60+60+60+60+60)
Train B would have already covered 480 Miles(80+80+80+80+80+80)
Now the distance between them is 480-420 = 60 miles

So 6 hours after its departure point Train B will be 60 miles ahead of Train A.

In your Solution,
You have solved the time for the train A,
But in Question they have asked the time for Train B
hence 7-1 = 6

Regards,
Uva.
Hello Uva,

Thanks for your reply. I now tried to approach this problem as follows:


Rate x Time = Distance
A: 60 x t = 60t
B: 80 x t = 80t

80t = 60t + 60
=> t = 3 hours


Rate x Time = Distance
A: 60 x t = d
B: 80 x t = d + 60

So, 80t = 60t + 60
=> 20t = 60
=> t = 3 hours

So, total time = 3 + 3 = 6 hours

Would this approach be correct? Thanks a lot.

Best Regards,
Sri
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by Uva@90 » Sat Oct 26, 2013 10:01 pm
gmattesttaker2 wrote:
Hello Uva,

Thanks for your reply. I now tried to approach this problem as follows:


Rate x Time = Distance
A: 60 x t = 60t
B: 80 x t = 80t

80t = 60t + 60
=> t = 3 hours


Rate x Time = Distance
A: 60 x t = d
B: 80 x t = d + 60

So, 80t = 60t + 60
=> 20t = 60
=> t = 3 hours

So, total time = 3 + 3 = 6 hours

Would this approach be correct? Thanks a lot.

Best Regards,
Sri

Sri,
Yes, after Three hour They meet each other and in three hours later they will be 60 KM away.

I will provide you another method,

As you know time = Distance/Speed

Now you have to note that, They are moving in the same direction.

hence speed will be their difference of Train B and Train A (If there are moving in towards each other then their speed is sum of both the trains)

Speed = 80-60 =20

and distance is,

Train A has already covered distance of 60 KM before train B has started and in addition to that Train B should also lead another 60 kn

so Distance is 60+60 =120 KM

So time is 120/20 = 6

Hope it helps

Regards,
Uva.
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by TheGmatTutor » Sun Oct 27, 2013 6:55 pm
The key to this problem is to use the difference in rates.

80 mph - 60mph = 20 mph

Thus, the second train is going 20 mph faster than the first. This means that for each hour that passes, it gains 20 miles on the first train. The second train starts out 60 miles behind, so it takes 3 hours to catch up. It then needs to get an additional 60 miles ahead, which takes another 3 hours. So the total time is 6 hours.
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by theCodeToGMAT » Mon Oct 28, 2013 9:25 am
Gap = 60

Time to catch = 60/(80-60) = 3 hrs

Time after meeting = 60/(80-60) = 3 hrs

Total Time = 6 hrs
R A H U L
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