<PRE><B>Question 117642</B>
THE SPEED OF AN AIRPLANE IN STILL AIR IS 224KM/H. THE PLANE TRAVELS 733KM AGAINST THE WIND AND 1075KM WITH THE WIND IN A TOTAL TIME OF 15 HR. WHAT IS THE SPEED OF THE WIND
:
Let x = wind speed
then
(224-x) = speed against the wind
and
(224+x) = speed with the wind
:
The total time is given as 15 hrs, write a time equation: Time = Dist/speed
:
Time with + time against = 15 hrs
{{{1075/((224+x))}}} + {{{733/((224-x))}}} = 15
:
Multiply equation by (224+x)(224-x) to get rid of the denominators, results
:
1075(224-x) + 733(224+x) = 15(224+x)(224-x)
:
240800 - 1075x + 164192 + 733x = 15(50176 - x^2)
:
-1075x + 733x + 240800 + 164192 = 752640 - 15x^2
:
+15x^2 - 342x + 404992 - 752640 = 0; arrange as a quadratic equation
:
15x^2 - 342x - 347648 = 0
:
Solve this using the quadratic formula; a=15, b=-342, c=-347648
:
I got a positive solution (approximately): x = 164.06 is the speed of the wind
:
Checking our solution:
224 - 164.06 = 59.94 km/hr against the wind
and
224 + 164.06 = 388.06 km/hr with the wind
:
1075/388.06 + 733/59.94 = 
2.77 + 12.23 = 15 hrs</PRE>