Evan flies a plane against a headwind for 4161 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Evan fly

Question

Evan flies a plane against a headwind for 4161 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Evan fly the plane when there is no wind?

Answer 1

v = speed of flight if no wind

 

u = wind speed = 8 mph

 

t = flight time against wind

 

t - 16 = flight time with help from wind

 

d = distance = 4161 miles

 

Outbound:

 

(v - 8) * t = 4161  [equation 1] 

 

Inbound:

 

(v + 8)(t - 16) = 4161  [equation 2]

 

Subtract equation 2 from equation 1 and get

 

(v - 8) * t - (v + 8)(t - 16) = 0

 

vt -8t -(vt -16v +8t -128) = 0

 

t(v - 8 - v - 8) - (-16v- 128) = 0

 

-16t = -(16v + 128)

 

t = v + 8

 

Substitute this result for t into equation 1 and get

 

(v - 8) * (v + 8) = 4161

 

v^2 - 64 = 4161

 

v = sqrt(4225) = 65 mph

 

t = v + 8 = 65 + 8 = 73 hrs