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#1**+1 **

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

CPhill Nov 11, 2017