You travel with a boat 90 km downstream with the current in 6 hours and back upstream
in 10 hours. Find the speed of the stream and the speed of the boat in still water, assuming
that the motion is uniform.
since distance = speed * time,
6(b+s)=90
10(b-s) = 90
To find the speed of the stream and the speed of the boat in still water, we can use the formula:
Boat speed in still water = (downstream speed + upstream speed) / 2 ........(1)
Stream speed = (downstream speed - upstream speed) / 2 ....................(2)
Let's start with finding the downstream speed.
Downstream speed = Distance / Time
Given that the distance traveled downstream is 90 km and the time taken is 6 hours:
Downstream speed = 90 km / 6 hours = 15 km/h
Similarly, we can find the upstream speed.
Upstream speed = Distance / Time
Given that the distance traveled upstream is 90 km and the time taken is 10 hours:
Upstream speed = 90 km / 10 hours = 9 km/h
Now, we can substitute these values into formulas (1) and (2) to find the boat speed in still water and the stream speed.
Boat speed in still water = (15 km/h + 9 km/h) / 2 = 12 km/h
Stream speed = (15 km/h - 9 km/h) / 2 = 3 km/h
Therefore, the speed of the stream is 3 km/h, and the speed of the boat in still water is 12 km/h.