Danny in his motorboat,took 3 hours to make a downstream trip with a current of 6 kph. The return trip upstream took 5 hours. What is the speed of the boat in still water?
What is the total travelled?
since distance = speed * time,
3(x+6) = 5(x-6)
Now just find x to get the speed.
To find the speed of the boat in still water, we can use the concept of relative velocity.
Let's assume the speed of the boat in still water is 'b' kph.
Downstream trip:
We know that the current is 6 kph and it aids the boat's speed. So, the effective speed of the boat in the downstream trip is (b + 6) kph. The time taken for this trip is 3 hours.
Using the formula: Speed = Distance/Time,
Distance = Speed * Time,
we can calculate the distance traveled in the downstream trip as:
Distance_downstream = (b + 6) * 3
Upstream trip:
In the upstream trip, the current opposes the boat's speed. So, the effective speed of the boat is (b - 6) kph. The time taken for this trip is 5 hours.
Using the same formula as before, we can calculate the distance traveled in the upstream trip as:
Distance_upstream = (b - 6) * 5
The total distance traveled is the sum of the distances in the downstream and upstream trips. So, we have:
Total distance = Distance_downstream + Distance_upstream
Substituting the values we have calculated, we get:
Total distance = (b + 6) * 3 + (b - 6) * 5
Simplifying this expression will give us the total distance traveled.
To calculate the speed of the boat in still water, we can use the formula: Speed_in_still_water = (Total_distance)/(Total_time).
Substituting the total distance and total time that we have calculated earlier, we can determine the speed of the boat in still water.