SOLUTION: David is traveling to the airport to catch a flight, if he travels at the speed of 30 mph, he is late by 13 minutes. If he travels at the speed of 40 mph, he will arrive 7 minutes

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Question 522689: David is traveling to the airport to catch a flight, if he travels at the speed of 30 mph, he is late by 13 minutes. If he travels at the speed of 40 mph, he will arrive 7 minutes earlier than the scheduled departure time of the flight. What is the distance to the airport (in miles)?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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David is traveling to the airport to catch a flight, if he travels at the speed of 30 mph, he is late by 13 minutes.
If he travels at the speed of 40 mph, he will arrive 7 minutes earlier than the scheduled departure time of the flight.
What is the distance to the airport (in miles)?
:
Let d = distance to airport
Let s = speed required to arrive on time
then
d%2Fs = the ideal time to the airport
:
Write a time equation for each scenario
:
d%2F30 - d%2Fs = 13%2F60; late
-d%2F40 + d%2Fs = 7%2F60; early
--------------------------------------- addition, eliminates d/s
d%2F30 - d%2F40 + 0 = 20%2F60
Clear denominators, multiply by 120, results:
4d - 3d = 2(20)
d = 40 mi to the airport
:
:
See if this works; find s
40%2F30 - 40%2Fs = 13%2F60;
mult by 60s, results
2s(40) - 60(40) = 13s
80s - 2400 = 13s
80s - 13s = 240
67s = 2400
s = 2400%2F67
s = 35.82 mph the ideal speed
:
Check solution in the late equation
40%2F30 - 40%2F35.82 =
1.3333 - 1.1167 = .2166 hr which is 13 min