To answer this question, it is necessary to use the definition of velocity, in order to get a two equations system
The answer is:
vb ( boat velocity ) = 3.5 m/h
vw ( water velocity) = 0.5 m/h
We know:
- v = d/t ( velocity is the distance travel over a certain period of time)
- velocity is a vector then if two velocities:
- have the same direction, you must add them to get the total velocity
- and subtract them, if they have opposite direction)
First trip, ( going to the picnic) both velocities have the same direction,
we call vb velocity of the boat, and vw the velocity of the water, then
3× vt = 12
vt = vb + vw
3 × ( vb + vw ) = 12 ⇒ 3×vb + 3×vw = 12 (1)
- Return trip, both velocities with opposite direction
vt = vb - vw ( we write vb - vw because they arrive at the beginning, meaning that vb > vw.
( 4× vt ) = 12
4 × ( vb - vw ) = 12 4×vb - 4×vw = 12 (2)
We have a two equations system
3×vb + 3×vw = 12
4×vb - 4×vw = 12
Solving for vb and vw
3×vb = 12 - 3×vw ⇒ vb = ( 12 - 3×vw / 3 ) ⇒ vb = 4 - vw
plugging that value in equation (2)
4 × ( 4 - vw ) - 4×w = 12 ⇒ 16 - 8 ×vw = 12
8 × vw = 4
Hence
vw = 4/8 miles per hour ⇒ vw = 0.5 m/h
and vb = 4 - 0.5
vb = 3.5 m/h
Related link : brainly.com/question/20052012
