SOLUTION: Hi I need your help answering the question. Airline Schedules allow 3 hours and 10 minuets airborne time to fly from Washington D.C to Dallas and 2 hours and 15 minuets from Dal

Question 254673: Hi I need your help answering the question.
Airline Schedules allow 3 hours and 10 minuets airborne time to fly from Washington D.C to Dallas and 2 hours and 15 minuets from Dallas to Washington D.C. The Time difference can largely be attributed to the jet stream, a wind that usually blows from west to east. The distance between Washington d.C and Dallas is 1176 miles. What is the speed of the jet stream? what is the speed of the plane in still air.
Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Airline Schedules allow 3 hours and 10 minutes airborne time to fly from Washington D.C to Dallas
and 2 hours and 15 minutes from Dallas to Washington D.C.
-------------------------------------------------------------------
The Time difference can largely be attributed to the jet stream, a wind that usually blows from west to east.
-------------------------------------------------------------------
The distance between Washington d.C and Dallas is 1176 miles.
--------------------------------------------------------------------
What is the speed of the jet stream? what is the speed of the plane in still air.
------
DC to DALLAS DATA:
distance = 1176 miles ; time = 3 1/6 hrs ; rate = 1176/(19/6) mph
-----------------------
DALLAS to DC DATA:
distance = 1176 miles ; time = 2 1/4 hrs ; rate = 1176/(9/4) mph
------------------------------
Equations:
plane + wind = 1176/(9/4)
Plane - wind = 1176/(19/6)
---
Add and solve for plane speed:
2p = 1176/(9/4) + 1176/(19/6)
p = 588/(9/4) + 588/(19/6)
p = 261 1/3 + 185.68
p = 447.02 mph (rate of the plane in still air)
--------------------------
Substitute into p+w = 1176/(9/4) to solve for "w":
447.02 + w = 1176/(9/4)
w = 75.65 mph (rate of the wind)
==========================================
Cheers,
Stan H.

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