The speed can be determined by taking the ratio of distance over time.
Speed= Distance / Time
If any of the two of these are known we can find the third one by solving the equation.
The speed of water current c is found to be 45 miles per hour.
The speed of the water current is required which can be found out by downstream and upstream speeds.
When the boat travels in the same direction as that of the current it is traveling downstream.
When the boat travels in the opposite direction to that of the current it is traveling upstream.
Suppose the speed of the boat downstream is d given by
Downstream speed= d = b + c
where b is the speed of boat and c is the speed of current .
Then the speed of the boat upstream is u given by
Upstream speed= u = b - c
The time the boat travels upstream is 1.5 hours longer than the
time it travels downstream.
Time upstream = 1.5 hours + time downstream
or
Distance upstream/ speed upstream =
1.5 + Distance downstream/ speed downstream
Putting the values:
40/30= 1.5 + 20/d
4/3- 1.5= 20/d
4- 4.5/3= 20/d
-0.5/3= 20/d
-0.5/60= 1/d
d= 60/-0.5
d= -120 miles per hour
The negative sign indicates that it is opposite to that of the given direction.
d= b+c ---------eq.1
u= b-c---------eq.2
Subtracting equation2 from eq.1
d-u= 2c
or
c= (d-u)/2
c= (120-30)/2
c= 90/2
c= 45 miles per hour
The speed of water current c is 45 miles per hour.
The boat speed can also be understood from the following.
https://brainly.com/question/10311710
