Photo:
THE MIRROR
Aliyah loves her little motor boat.
She lives on a river and loves to cruise downriver to the spectacular rock in the middle of the river.
It takes her 20 minutes to get there.
On the way back she has to ride against the current, but that doesn't mean she accelerates any further.
She sets the throttle to the same level as when driving to the rock.
Because of the current, the return trip takes exactly twice as long: 40 minutes.
If there were no current, how long would Aliya's jaunt from home to the rock take?
Aliyah would be
26 minutes and 40 seconds
on the road.
At first glance, the task hardly seems solvable.
We don't know the length of the route or the flow rate of the river.
But the problem can actually be cracked.
You know: speed is distance through time.
With
v
we denote the speed of the boat in the water (without current), the river has the current speed
a
.
The distance to the rock has the length
s
.
On the outward journey, the speed of the boat in the water and the flow speed add up:
v+a = s/20min
On the way back we have to subtract the flow rate from the speed of the boat in the water:
va = s/40 min
We add the two equations and get:
2*v = s/20min + s/40min = 3*s/40min
Let's reformulate that a bit:
v = s / (1/3 * 80min)
Now we're almost done.
In water with no current, the following applies:
v = s/t
And switched to t:
t = s/v
We can calculate
s/v directly using the equation above
v = s / (1/3 * 80 min) :
t = s/v = 1/3 * 80 min = 26 min 40 sec
What we cannot calculate is the flow velocity a and the speed of the boat in the water v.
But they weren't even asked.
Many thanks to the reader Wilfried Keesseler who suggested this puzzle.
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