<PRE><B>Question 148676</B>
A plane leaves an airport and flies south at 188 mph. Later, a second plane leaves the same airport and flies south at 470mph. If the second plane overtakes the first one in 2.5 hours, how long of a head start did the first plane have? 
:
Let t = head start time in hrs
:
When one plane overtakes the other plane. they will have traveled the same distance
Write a distance equation from this fact: Dist = speed * time
:
2nd plane travel time = 2.5 hrs
1st plane travel time = (t+2.5)
:
188(t+2.5) = 470 * 2.5
:
188t + 470 = 1175
:
188t = 1175 - 470
:
188t = 705
t = {{{705/188}}}
t = 3.75 hr head start
:
:
Check the solution by confirming that each plane traveled the same distance
1st plane travel time: 2.5 + 3.75 = 6.25
:
188 * 6.25 = 1175 mi
470 * 2.5  = 1175 mi</PRE>