SOLUTION: I would really appreciate any help I could get on this question. Word problems are sooo very challenging sometimes and I just cannot figure out how to do this one :<( An airpla

Question 73230: I would really appreciate any help I could get on this question. Word problems are sooo very challenging sometimes and I just cannot figure out how to do this one :<(
An airplane took 2.5 hours to fly 625 miles with the wind. It took 4 hours and 10 minutes to make the return trip against the same wind. Find the wind speed and the speed of the plane in still air.
(All I can see is that if you convert both times traveled into minutes then there is a 100 minute difference and divided by 625 miles would be 6.25 miles per minute but which part of the question would this answer and is it even relevent to either question??)
Thanks so much in advance for any help that can be provided :>)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An airplane took 2.5 hours to fly 625 miles with the wind. It took 4 hours and 10 minutes to make the return trip against the same wind. Find the wind speed and the speed of the plane in still air.
:
you probably want to keep it in hrs since the speed is given in mph (altho you could convert that to mi/min) Converting 10 min to hrs is a slight problem since it produces a repeating decimal, however let's go that route.
:
4 hrs and 10 min: 10/60 = .167 hrs so we have 4.167 hrs
:
Let x = speed of the plane in calm air
Let y = speed of the wind
:
The speed over ground:
Against the wind: (x-y)
With the wind: (x+y)
:
Make two distance equations: time * speed = distance
:
2.5(x + y)) = 625; (with the wind)
Simplify: divide both sides by 2.5
x + y = 625/2.5
x + y = 250
x = (250 - y); use this for substitution in our 2nd equation
:
The 2nd equation (against the wind)
4.167(x - y) = 625
Substitute (250-y) for x and solve for y:
4.167((250-y) - y) = 625
4.167(250-2y) = 625
1041.75 - 8.334y = 625
-8.334y = 625 - 1041.75
-8.334y = -416.75
y = -416.75/-8.334
y = + 50.006 mph is the wind, call it 50 mph
:
Find x:
x = 250 - y
x = 250 - 50
x = 200 mph is the plane speed in still air
:
:
Always check the solutions in the original problem:
Speed with the wind = 250
Speed against the wind = 150
:
2.5(250) = 625
4.167(150) = 625.05 (that repeating decimal comes back to haunt us)
:
:
Looking at the statement:
(All I can see is that if you convert both times traveled into minutes then there is a 100 minute difference and divided by 625 miles would be 6.25 miles per minute but which part of the question would this answer and is it even relevant to either question??)
:
There is a certain logic in what you say, however, it does not do anything for
us. It is interesting in that if you convert 6.25 mi to mph you have 375 mph
which is twice the average speed of the whole trip; 1250/(2.5+4.127) = 187.5
Just an observation on my part; does not really pertain to the problems so ignore it if it tends to confuse you.
:
Hope the problem procedure made sense to you, any questions, email me.

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