Skip to main content
Posts
A rower rows regularly on a river, from A to B and back. He’s got into
the habit of rowing harder when going upstream, so that he goes twice as
fast relative to the water as when rowing downstream.
One day as he’s
rowing upstream he passes a floating bottle. He ignores it at first but
then gradually grows curious about its contents. After 20 minutes of
arguing with himself he stops rowing and drifts for 15 minutes. Then he
sets out after the bottle. After some time rowing downstream he changes
his mind, turns around, and makes his way upstream again. But his
curiosity takes hold once more, and after 10 minutes of rowing upstream
he turns and goes after the bottle again. Again he grows ashamed of his
childishness and turns around. But after rowing upstream for 5 minutes
he can’t stand it any longer, rows downstream, and picks up the bottle 1
kilometer from the point where he’d passed it.
How fast is the current?
That's the speed of water current!
What was the story?
Just for a moment let's assume the rower is rowing on a calm lake where water is stationary. Then, the bottle that he saw is also not moving & floating at one point.
In the case, he moves away (upstream in real case) from the bottle & comes back (downstream in real case) again to collect the bottle. He rows away from the bottle for 20 + 10 + 5 = 35 minutes.
Remember his speed is double when he goes away from bottle than when he is coming towards the bottle. That's why he takes 35 X 2 = 70 minutes to come back at the point where bottle is floating.
Moreover, he drifts for 15 minutes in real case; for that let's assume he sits motionless for 15 minutes (in our assumed lake case) at some point in between.
So after leaving the bottle, he returns to the bottle after 35 + 15 + 70 = 120 minutes.
Now, assume this water in the lake is moving and this bottle is 'displaced' by 1 KM away from it's original position in 120 minutes.
That means, the water is moving at the speed of 1 km / 120 minutes. That is the speed of water current is 1/2 kmph.
You and I have to travel from Startville to Endville, but we have
only one bicycle between us. So we decide to leapfrog: We’ll leave
Startville at the same time, you walking and I riding. I’ll ride for 1
mile, and then I’ll leave the bicycle at the side of the road and
continue on foot. When you reach the bicycle you’ll ride it for 1 mile,
passing me at some point, then leave the bicycle and continue walking. And
so on — we’ll continue in this way until we’ve both reached the
destination.
Will this save any time?
You say yes: Each of us is riding for part
of the distance, and riding is faster than walking, so using the bike
must increase our average speed.
I say no: One or the other of us is always walking; ultimately every
inch of the distance between Startville and Endville is traversed by
someone on foot. So the total time is unchanged — leapfrogging with the
bike is no better than walking the whole distance on foot.
Who’s right?
Look who is right in the case!
Where I went wrong?
That's going to save time for sure.
Let's assume that the distance between Startville and Endville is 2 miles. And suppose we walk at the same speed of 4 mph and ride bicycle at the speed of 12 mph.
Then I will travel for first 1 mile in 5 minutes leave the bicycle and start walking thereafter. You take 15 minutes to reach at the point to pick up bicycle and ride next mile. For next mile, I need 15 minutes as I am walking & you need only 5 minutes ride on bicycle. So exactly after 20 minutes we will reach at Endville.
And what if we had walked entire 2 miles distance? It would have taken 30 minutes for us to reach at the destination.
One thing you must have noticed, each of us walked for 1 mile only and ride on bicycle for other mile which saved 10 minutes of our journey. Imagine it as if we had 2 bicycles where we ride 1 mile in 5 minutes, leave bicycles and walk next mile in another 15 minutes.
So my argument in the case is totally wrong. It would have been correct if I had waited for you after finishing 1 mile ride on bicycle and then started to walk next mile.
In that case, you will reach at the destination in 20 minutes but I need 30 minutes as I wasted 10 minutes in middle.
Conclusion:
My argument -
"One or the other of us is always walking; ultimately every inch of the
distance between Startville and Endville is traversed by someone on
foot."
tells only half story.
Yes, ultimately every inch of the
distance between Startville and Endville is traversed by someone on
foot but the distance that each of us walk is equal though different parts of journey. And for the rest of distance we ride on bicycle where total time required for journey is saved.
