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# More help? <3

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Thank you CPhill you're thebest!!!!!!!!!!!!!!!!!!!!! <3

Nov 11, 2017
edited by Supergirl  Nov 11, 2017
edited by Supergirl  Nov 11, 2017

#1
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a) Represent as a rational expression the time going to Germany.

The plane is being slowed by the wind so its rate is x - 50

The time going to Germany is  ....... Distance / Rate  =   9900 / [ x - 50]

b) Represent as a rational expression the time returning.

The plane is helped by the wind on the return trip....so its rate is  x + 50

And the time returning plus 4 hrs  = time going to Germany....so....we can represent (b) as

9900 / [ x + 50] + 4  =    [9900 + 4 [ x + 50] ]  / [ x + 50 ]

c) Write an equation representing the relationships between the times.

We have that

9900 / [ x - 50] =    [9900 + 4 [ x + 50] ]  / [ x + 50 ]

d) What was the average rate of the plane in still air.

9900 / [ x - 50]  =  [  9900  + 4x + 200 ] / [ x + 50 ]       cross-multiply

9900 [ x + 50 ]  =  [ 10100 + 4x] [ x - 50]

9900x + 495000 =  10100x + 4x^2 - 505000 - 200x

9900x + 495000 =  9900x + 4x^2 - 505000      rearrange as

4x^2  - 1000000  =  0      divide through by 4

x^2   - 250000  = 0

x^2  =  250000            take the positive root of both sides

x =  500 km/ hr  =   speed in still air

e) How long did the round trip take?

Total time is   twice the return time plus 4 hours =   2 [  9900 / [ x + 50]   ]  + 4  =

2 [ 9900 / 550 ] +  4  =

36   + 4  =     40  hrs

Nov 11, 2017
#2
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CPhill: 9,900 km is "round trip." One-way trip should be=9,900/2=4,950 km.

Nov 11, 2017