A boat travels 30 km upstream in 5 hours and 24 km downstream in 3 hours. Find the speed of th

step 1 Hi, here in this given problem, suppose speed of the boat in still water, that is VB, and speed

A boat travels 30 km upstream in 5 hours and 24 km...

A boat travels $30 \mathrm{~km}$ upstream in 5 hours and $24 \mathrm{~km}$ downstream in 3 hours. Find the speed of the boat in still water and the speed of the water current (A) $7 \mathrm{kmph}, 2 \mathrm{kmph}$ (B) 14 kmph, 1 kmph (C) $7 \mathrm{kmph}, 1 \mathrm{kmph}$ (D) $8 \mathrm{kmph}, 2 \mathrm{kmph}$

A boat travels $30 \mathrm{~km}$ upstream in 5 hours and $24 \mathrm{~km}$ downstream in 3 hours. Find the speed of the boat in still water and the speed of the water current
(A) $7 \mathrm{kmph}, 2 \mathrm{kmph}$
(B) 14 kmph, 1 kmph
(C) $7 \mathrm{kmph}, 1 \mathrm{kmph}$
(D) $8 \mathrm{kmph}, 2 \mathrm{kmph}$

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Key Concepts

Relative Speed in Fluids

This concept involves understanding how an object’s speed is affected by the medium through which it moves. In the context of boats in water, the boat's effective speed is either increased or decreased by the rate of the current, depending on whether it is moving downstream (with the current) or upstream (against the current). This idea is central to solving problems where both the motion of the object and the motion of the medium must be considered.

Rate-Time-Distance Relationship

This fundamental concept in kinematics states that distance is the product of speed and time. It is used to derive effective speeds by dividing the distances traveled by the time taken, which then allows the formation of equations that relate the boat's speed in still water and the speed of the current.

Systems of Equations

When given multiple conditions or scenarios, such as upstream and downstream travel, a system of equations can be used to represent the relationships between the variables (here, the boat's speed in still water and the current’s speed). Solving these simultaneous equations using methods such as substitution or elimination helps determine the values of the unknown variables.

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