help please

Thanks, jc........here's another way

 

Let r be Brittany's normal rate   and w be the  wind speed....and Distance / Rate = Time....so......

 

700 /[ r + w]  =  12  →  700  = 12r + 12w  →  700 - 12r  = 12w   → [ 700 - 12r]/ 12    = w   (1)

 

700/ [r - w] = 14    (2)

 

Substituting (1)  into (2)  for  w, we have in the denominator

 

r - [700 -12r] / 12    =   [12r - 700 + 12r]/12   =  [24r - 700] / 12 .....and we have

 

700  / ([ 24r - 700] / 12)  = 14

 

12* 700  =  14 [ 24r - 700]

 

26(700) = 14*24r     and solving for r, we have

 

r = 54.167 km/hr

 

And the wind speed is given by :

 

w =   [700 - 12(54.167)'] / 12   = about 4.166  km/hr

From A to B   Rate = 700/12 = 58.33   This equals her speed PLUS wind speed

(assuming the wind speed is added to her speed and subtracted from her speed)

From B to A    Rate = 700/14 = 50 km/hr  this equals her speed MINUS wind speed

 

Bike + wind = 58.33

Bike - wind = 50.

 

Add them together

 

2 bike = 108.33

Bike speed = 108.33/2 = 54.17 km/hr

Bike + wind = 58.33

54.17 + wind = 58.33

Wind speed = 58.33- 54.17 = 4.16 km/hr

 

~jc

700/12=58.33kph-Brittany's average speed from A to B

700/14=50.00kph-Brittany's average speed from B to A

58.33 - 50=8.33kp-differnce in speed due to wind

But it slowed her down by 2 hours, therefore this slowdown is due to:

8.33/2=4.16 kph- being the wind speed.