SOLUTION: Tanya, who is a long distance runner, runs at an average velocity of 8 miles per hour. Two hours after Tanya leaves your house, you leave in your Honda and follow the same route. I

Question 27286: Tanya, who is a long distance runner, runs at an average velocity of 8 miles per hour. Two hours after Tanya leaves your house, you leave in your Honda and follow the same route. If your average velocity is 40 miles per hour, how long will it be before you catch up with Tanya? ow far will each of you be from your house?
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Tanya, who is a long distance runner, runs at an average velocity of 8 miles per hour. Two hours after Tanya leaves your house, you leave in your Honda and follow the same route. If your average velocity is 40 miles per hour, how long will it be before you catch up with Tanya? ow far will each of you be from your house?
Let Tanya run y miles and reach the post A
Her running speed is 8 miles per hour.
In 1 hour she runs 8 miles.
That is 8 miles are covered in 1 hour.
Therefore 1 mile is covered in 1/8 of an hour.
Hence y miles are covered in (1/8) X y = y/8 hours
Two hours after Tanya leaves, I leave on the Honda and my speed is 40 miles per hour. And I catch up with Tanya. That is I reach the post A
In one hour I ride 40 miles.
That is 40 miles are covered in 1 hour.
Therefore 1 mile is covered in 1/40 of an hour.
Hence y miles are covered in (1/40) X y = y/40 hours.
But there is a time lapse of 2 hours between Tanya's running and my riding
Therefore Tanya's hours - my hours in travelling the same distance y miles is 2 hours.
Therefore y/8 - y/40 = 2
Multiplying by 40(which is the lcm of 8 and 40)
(y/8) X 40 - (y/40) X 40 = 2 X40
implies 5y - y = 80
That is 4y = 80
Dividing by 4 we get y = 20
Thus it will be 20 miles from the house to the post A
where I caught up with Tanya.
Verification:
Tanya travels 8 miles in 1 hour.
Therefore she will cover 20 miles in (1/8) X 20 = 20/8 = 5/2 hours.
I ride 40 miles in 1 hour.
Therefore I will cover 20 miles in (1/2) an hour.
So leaving the house 2 hours after Tanya leaves I ride for (1/2) an hour and catch up with her 2 and a (1/2) hours target to reach the Post A

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