Tom was floating down the river on a raft when, 1km down, Michael took to the water in a rowing boat. Michael rowed downstream at his fastest pace. Then he turned around and rowed back, arriving at his starting point just when Tom drifted by.
If Michael's rowing speed in still water is ten times the speed of the current in the river, what distance had Michael covered before he turned his boat around?
Where was Tom when Michael started rowing? He must have been farther upstream at the time. I will assume Tom was one km upstream when Michael started rowing.
Let v = the river speed and V = 10v be Michael's speed in still water.
Michael rows downstream at a land speed v + V = 11 v and upstream at a land speed of V-v = 9 v. Tom travels at speed v (by floating)
Let T be the time they both are on the water between when Michael starts and finishes rowing.
Let t be the time Micheal rows downstream; T-t is the time he rows upstream
v T = 1 km
11 v t = 9 v (T-t)= 9 - 9 vt
20 vt = 9
vt = 0.45 km
So Tom floated 0.45 km while Micheal rowed downstream and 0.55 km while he rowed upstream. Since Micheal rowed downstream 11 times faster than Tom floated, he would have travelled 11*0.45 = 4.95 km in that time
dfh
To answer this question, we need to break it down into a few key steps:
Step 1: Determine the speed of the current in the river.
Given that Michael's rowing speed in still water is ten times the speed of the current, let's assign a variable to the speed of the current. Let's say the speed of the current is "x." Therefore, Michael's rowing speed in still water would be "10x."
Step 2: Calculate the time it takes for Tom to float 1 km downstream.
Since Tom is floating downstream, we can assume that his drift speed is the same as the speed of the current, which is "x." Therefore, it takes Tom 1 km / x km/hr = 1/x hours to travel 1 km downstream.
Step 3: Calculate the time it takes for Michael to row downstream and back to his starting point.
Since we know Michael's rowing speed in still water is "10x," when he is rowing downstream, his effective speed is (10x + x) = 11x. Since Michael's effective speed is 11x and he covers the same distance as Tom (1 km) before they meet, we can deduce that it took Michael 1 km / (11x) hr = 1/(11x) hours to row downstream.
To return back to his starting point, Michael will now be rowing against the current. Hence, his effective speed will be (10x - x) = 9x. It took 1/(11x) hours for Michael to row downstream, so it will take the same amount of time for him to row upstream.
Step 4: Calculate the distance Michael had covered before turning around.
Since Michael's speed rowing upstream (9x) is the same as his speed rowing downstream (11x), we can calculate the distance he covered by multiplying his speed with the time it took him to row downstream.
Distance = Speed * Time
Distance = (11x) * (1/(11x))
Distance = 1 km
So, Michael covered a distance of 1 km before turning his boat around.