Marcia flew her ultra-light plane to a nearby town against the headwind of 15 km per hour in 2 hours and 20 minutes. the return trip under the same wind conditions took an hour 24 minutes. find the planes are speed and distance to the nearby town

Speed= 60 km/h

Distance to the nearby town= 105 km

Step-by-step explanation:

Given: Wind speed= 15 km/h

           Time taken while going = 2 h 20 minutes.

           Time taken while returning = 1 h 24 minutes

First we will get the time in uniform unit of hours,

we will convert minutes in hours for to get

∴

Similarly for

∴

Now, lets take Plane´s speed as a and distance as d.

While going to the nearby town it is headwind,

∴

While returning it is tailwind

 ∴

Next, we will use the formula,

As distance remain same:

⇒

Now, divide both side by 7

⇒

cross multiplying both side

⇒

∴

Speed of plane is 60 km/h

Now substituting the value of a in either of equation to get distance.

∴ d=

105 km is the distance to the nearby town.