Problema Solution
A hot air balloon travels 40 miles against the wind in the same amount of time that it travels 200 miles with the wind. if the speed of the wind is 20 mphˏ how fast does the hot air ballon travel against the wind.
Answer provided by our tutors
let
v = the speed of the balloon in still air
w = 20 mph the speed of the wind
v - w = the speed against the wind
v + w = the speed with the wind
we will use the formula speed = distance/time
A hot air balloon travels 40 miles against the wind in the same amount of time that it travels 200 miles with the wind
40/(v - w) = 200/(v + w)
that is
40/(v - 20) = 200/(v + 20)
by solving we find
v = 30 mph
click here to see the step by step solution of the equation
the speed against the wind is: v - w = 30 - 20 = 10 mph
the hot air balloon travels with 10 mph against the wind.