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Time taken to be 40 miles apart?

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by gmattesttaker2 » Sat Oct 26, 2013 5:08 pm
Hello,

Can you please assist with this :

Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?

My approach was as follows:

Rate x Time = Distance

Paul: 4 x t = 4t
Mary: 5 x (t-1) = 5(t-1)

So, 4t + 5(t-1) = 40
=> 4t + 5t - 5 = 40
=> 9t = 45
=> t = 5

I was thinking something on these lines:

4 x 5 = 20
and 5 x (5-1) = 20

So, t = 9 hours

However, I don't think this is correct? Can you please assist? Thanks a lot.
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by Brent@GMATPrepNow » Sat Oct 26, 2013 8:37 pm
gmattesttaker2 wrote:
Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?
For the 1st hour, Paul is the only person moving.
He moves at 4 mph, so after the 1st hour, they are 4 miles apart.


Now Mary leaves.
So, each hour the distance between them increases by 9 miles (since 5 mph + 4 mph = 9 mph).
So, after 4 additional hours, hours the distance between them is increased by 36 miles

So, after a total of 5 hours, they are 40 miles apart (since 4 miles + 36 miles = 40 miles)

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Oct 26, 2013 8:44 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this :

Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?

My approach was as follows:

Rate x Time = Distance

Paul: 4 x t = 4t
Mary: 5 x (t-1) = 5(t-1)

So, 4t + 5(t-1) = 40
=> 4t + 5t - 5 = 40
=> 9t = 45
=> t = 5

At this point, you are done
t = 5, which means it takes 5 hours for the two people to be 40 miles apart.
DONE!

I was thinking something on these lines:

This next part proves that your answer is correct
4 x 5 = 20 (so Paul's total distance traveled = 20 miles)
and 5 x (5-1) = 20 (so Mary's total distance traveled = 20 miles)
Since both people traveled 20 miles, they are 40 miles apart . . . Perfect!


So, t = 9 hours No. All this means is that Paul traveled for 5 hours and Mary traveled for 4 hours. We get a total of 9 hours, but the question doesn't ask us to find the sum of the travel times
Hey Sri,

Your solution is perfect.
You just went off track at the very end.
My comments are in green.

Cheers,
Brent
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by gmattesttaker2 » Sun Oct 27, 2013 8:47 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this :

Paul and Mary start getting away from each other from the same point along a straight line.
Paul travels at 4 mph while Mary travels at 5 mph. If Mary started travelling one hour later, how long will it take them to be 40 miles apart?

My approach was as follows:

Rate x Time = Distance

Paul: 4 x t = 4t
Mary: 5 x (t-1) = 5(t-1)

So, 4t + 5(t-1) = 40
=> 4t + 5t - 5 = 40
=> 9t = 45
=> t = 5

At this point, you are done
t = 5, which means it takes 5 hours for the two people to be 40 miles apart.
DONE!

I was thinking something on these lines:

This next part proves that your answer is correct
4 x 5 = 20 (so Paul's total distance traveled = 20 miles)
and 5 x (5-1) = 20 (so Mary's total distance traveled = 20 miles)
Since both people traveled 20 miles, they are 40 miles apart . . . Perfect!


So, t = 9 hours No. All this means is that Paul traveled for 5 hours and Mary traveled for 4 hours. We get a total of 9 hours, but the question doesn't ask us to find the sum of the travel times
Hey Sri,

Your solution is perfect.
You just went off track at the very end.
My comments are in green.

Cheers,
Brent

Hello Brent,

Thank you very much for going over my solution and for your very detailed and excellent explanation (as always). Thanks again for your help.

Best Regards,
Sri
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by theCodeToGMAT » Mon Oct 28, 2013 9:30 am
Another Approach

Time = GAP/Sum of Speed = (40-4)/(4+5) = 36/9 = 4

Total Time = 4+1 = 5 hours
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