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)?
:
Let d = distance to airport
Let s = speed required to arrive on time
then
{{{d/s}}} = the ideal time to the airport
:
Write a time equation for each scenario
:
 {{{d/30}}} - {{{d/s}}} = {{{13/60}}}; late
-{{{d/40}}} + {{{d/s}}} = {{{7/60}}}; early
--------------------------------------- addition, eliminates d/s
{{{d/30}}} - {{{d/40}}} + 0 = {{{20/60}}}
Clear denominators, multiply by 120, results:
4d - 3d = 2(20)
d = 40 mi to the airport
:
:
See if this works; find s
 {{{40/30}}} - {{{40/s}}} = {{{13/60}}}; 
mult by 60s, results
2s(40) - 60(40) = 13s
80s - 2400 = 13s
80s - 13s = 240
67s = 2400
s = {{{2400/67}}}
s = 35.82 mph the ideal speed
:
Check solution in the late equation
{{{40/30}}} - {{{40/35.82}}} = 
1.3333 - 1.1167 = .2166 hr which is 13 min