Snoopy flies his Sopwith Camel the 120 kilometers from Londo

Snoopy flies his Sopwith Camel the 120 kilometers from London to Calais in 12 hours, flying into a headwind. The return trip, with the same wind as a tailwind, takes only 2 hours. How fast is Snoopy flying throught the air? How fast is the wind blowing?

Solution

Let the speed of the Airplane be x
Let the speed of the wind be y
12(x-y)=120 (first equation)
2(x+y)=120 (second equation)
Solve for y in the 2nd equation:
2x+2y=120
2y=120-2x
y=60-x (subsitution)

From first equation:
12x-12y=120
Subsitute for y:
12x-12(60-x)=120
12x-720+12x=120
24x=840
x=35
y=60-35
y=25

Hence, he is flying at rate of 35mph with wind blowing at 25mph.