Imelda's plane travels at a speed of 350kph in still air. One day, she travels 169km against the wind at the same time it takes to travel 190km with the wind. Find the speed of the wind.
speed of wind --- x km/h
speed against the wind = 350-x km/h
speed with he wind = 350+x km/h
169/(350-x) = 190/(350+x)
cross-multiply and solve for x
To find the speed of the wind, we can set up a system of equations based on the given information.
Let's assume the speed of the wind is 'w' kph.
When Imelda is flying against the wind, her effective speed is reduced by the speed of the wind. So, her speed in this case would be (350 - w) kph.
When Imelda is flying with the wind, her effective speed is increased by the speed of the wind. So, her speed in this case would be (350 + w) kph.
Now, we are given that:
Time taken to travel 169 km against the wind = Time taken to travel 190 km with the wind.
To find these times, we can divide the respective distances by the respective speeds:
Time against the wind = Distance against the wind / Speed against the wind
Time against the wind = 169 km / (350 - w) kph
Time with the wind = Distance with the wind / Speed with the wind
Time with the wind = 190 km / (350 + w) kph
Since these two times are equal, we can set up the equation:
169 / (350 - w) = 190 / (350 + w)
To solve this equation, we can cross-multiply:
169(350 + w) = 190(350 - w)
Now we can simplify and solve for 'w'.