Armando flies a plane against a headwind for 3445 miles. The return trip with the wind took 12 hours less time. If the wind speed is 6 mph, how fast does Armando fly the plane when there is no wind?

Question

Armando flies a plane against a headwind for 3445 miles. The return trip with the wind took 12 hours less time. If the wind speed is 6 mph, how fast does Armando fly the plane when there is no wind?

Answer 1

3445 = (r-6)* t = rt - 6t

3445 = (r+6)(t-12) = rt - 12r + 6t - 72

Subtracting these equations: 0 = -12r + 12t - 72

72 = 12t - 12r

6 = t - r

t = r+6

Plugs into 1st equation:

3445 = (r-6)(r+6)

3445 = r^2 - 36

3481 = r^2

r = 59

3445 = (59+6)* t

3446 = 65 * t

t = 53

3445 = (59-6)*t

3445 = 53*t

t = 65

notice that is 12 hours difference..

59 mph

not a very fast airplane... cars go faster than that