# Explain these 2 doubts for this boat & streams problem

#### Ganesh Ujwal

A girl was travelling in a boat, suddenly wind starts blowing and blows her hat and started floating back downstream. The boat continued to travel upstream for 12 more minutes before she realized that her hat had fallen off. She turned back downstream and she caught her hat as soon as she reached the starting point. If her hat flew off exactly 2 km from where she started. What is the speed of the water?

the speed of the boat; X
the speed of the current; Y

BC’s distance = boat upstream time*boat upstream speed; 12(X-Y)
CA’s distance = t(X+Y)
AB's distance = (12+t)Y

AB + BC = CA
(12+t)Y+12(X-Y)= t(X+Y)

t = 12

S = 2/24 min = 5 kmph

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Why CA = t(X+Y) ? why not (12+t)(X+Y)?

Why AB = (12+t)Y? why not just 12y?

How 24 min in last step?

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#### skipjack

Forum Staff
As t is the time for the boat to return from C to A, it shouldn't have 12 minutes added to it when considering that journey.

The hat started floating back from B to A 12 minutes before the boat turned back, so the hat's return took 12 minutes + t, which equals 24 minutes, because t is found to be 12. minutes.

The letter S should be Y, so Y = 2km/(24 minutes) = (1/12)km/minute = 5 kmph.

#### Ganesh Ujwal

As t is the time for the boat to return from C to A, it shouldn't have 12 minutes added to it when considering that journey.
Does it mean t already contains 12 mins in it?

#### skipjack

Forum Staff
No. That's why 12 minutes is added to it when the hat's return from B to A is considered.

#### Ganesh Ujwal

No. That's why 12 minutes is added to it when the hat's return from B to A is considered.
In the diagram, CA contains BA. But in t, why 12 mins not included?
Its pretty obvious, t > 12.

#### skipjack

Forum Staff
The given solution should have explicitly defined t as the time the boat took to travel from C to A. This journey was made at a constant speed (X + Y). It was preceded by the boat's journey from B to C, which was made at a different constant speed (X - Y). The boat's journey from B to A via C wasn't made at a constant speed, but the hat's journey from B to A occurred simultaneously and was at a constant speed , Y (the speed of the current). The solution proceeds by writing the distance = time × speed equation for each of the constant speed journeys that I have just mentioned, using X as the boat's speed relative to the water.

#### Ganesh Ujwal

From B, boat took 12 mins to reach C. Am I right?

From that C, boot took 12 mins to reach A for fetch a hat ? Am I right?

#### skipjack

Forum Staff
Yes (for first question). Hence the first equation in the solution.

Yes (for second question), but this time has to be calculated during the solution process.

Ganesh Ujwal