Algebra without a clue

Question

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air

Answer 1

We assume that the effective speed into a headwind is (planespeed - headwind) and effective speed with a tailwind is (plane speed + tailwind).

So, assuming the headwind in one direction is the same magnitude as the tailwind in the other,

planespeed + wind = 158 km/h

planespeed - wind = 112 km/h

Two equations in two unknowns:

add the two to get 2*planespeed = 270

planespeed = 135

Then, Becky, substitute into either equation and solve for wind speed.

Answer 2

The problem cannot be solved due to a lack of information.

There are three unknowns, plane speed, wind speed, and time of flights.

Yet only the rate is known.