SOLUTION: Tanya, who is a long distance runner, runs at an average velocity of 8mph. two hours after Tanya leaves your house, you leave in your Honda and follow the same route. If your avera

Question 267630: Tanya, who is a long distance runner, runs at an average velocity of 8mph. two hours after Tanya leaves your house, you leave in your Honda and follow the same route. If your average velocity of 40mph, how long will it be before you catch up with Tanya? How far will you be from your home?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
runs at an average velocity of 8mph.
two hours after Tanya leaves your house, you leave in your Honda and follow the same route.
If your average velocity of 40mph, how long will it be before you catch up with Tanya?
:
Find the time required to catch up with the runner first
when that happens both will run the same distance, write a distance equation: Dist = speed*time
:
Let t = Honda's travel time
then
(t+2) = Runner's travel time
:
honda's dist = runner's dist
40t = 8(t+2)
40t = 8t + 16
40t - 8t = 16
32t = 16
t =
t = .5 hrs, Honda's travel time (2.5 hrs = runner's travel time)
:
How far will you be from your home?
:
Find the dist using the Honda time:
.5(40) = 20 mi
Check the dist using the runner's time
2.5(8) = 20 mi also
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