Question

LAn airplane takes 5 hours to travel a distance of 3800 kilometers against the wind. The return trip takes 4 hours with the wind. What is the rate of the plane instill air and what is the rate of the wind?

Answer 1

95076Solution

For this case we can create the following notation:

a= airplane speed =

w= wind speed

a+w = velocity with wind speed

a-w= velocity against wind speed

The definition of Distance is given by:

d= vt

Solving for t we got:

t= d/v

Using the information given we have these conditions:

d= 3800 km

4= 3800/ (a+w)

Solving we have:

4a +4w = 3800

Dividing by 4 both sides we got:

a+w= 950 (1)

5= 3800/ (a-w)

5a -5w = 3800

a-w = 760 (2)

Solving for a from the second equation we have:

a= 760+w (3)

And replacing into the first equation we got:

760+w +w= 950

2w=190

w= 95

a= 855

a+w=