Question

Q. A boat can go 65 km upstream in 5 hrs. and 69 km downstream in 3 hrs. Find the speed of the boat in still water.
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Answer 1

AnswEr :

$\bf{\green{\large{\underline{\underline{\bf{Given\::}}}}}}$

A boat can go 65 km upstream in 5 hours and 69 km downstream in 3 hours.

$\bf{\red{\large{\underline{\underline{\bf{To\:find\::}}}}}}$

The speed of the boat in still water.

$\bf{\blue{\Large{\underline{\underline{\rm{Explanation\::}}}}}}$

Let the speed of the boat be R km/h

Let the speed of the stream be M km/hr

$\bf{\orange{\Large{\underline{\underline{\sf{\blacksquare{1st\:Case\::}}}}}}}$

$\bf{We\:have}\begin{cases}\sf{A\:boat\:speed\:for\:upstream=(R-M)km/hr}\\ \sf{Time\:=\:5\:hours\\ \sf{Distance=65\:km}\end{cases}}$

A/q

Formula use :

$\bf{\large{\boxed{\sf{Time=\frac{Distance\:}{Speed} }}}}}}$

$\mapsto\tt{5=\dfrac{65}{R-M} }\\\\\\\\\mapsto\tt{5(R-M)=65}\\\\\\\\\mapsto\tt{R-M=\cancel{\dfrac{65}{5} }}\\\\\\\\\mapsto\tt{R-M=13}\\\\\\\\\mapsto\tt{\red{R=13+M.............................(1)}}$

$\bf{\orange{\Large{\underline{\underline{\sf{\blacksquare{2nd\:Case\::}}}}}}}$

$\bf{We\:have}\begin{cases}\sf{A\:boat\:speed\:for\:downstream=(R+M)km/hr}\\ \sf{Time\:=\:3\:hours\\ \sf{Distance=69\:km}\end{cases}}$

So,

$\mapsto\tt{3=\dfrac{69}{R+M} }\\\\\\\\\mapsto\tt{3(R+M)=69}\\\\\\\\\mapsto\tt{R+M=\cancel{\dfrac{69}{3} }}\\\\\\\\\mapsto\tt{R+M=23}\\\\\\\\\mapsto\tt{13+M+M=23\:\:\:\:\:\:\:\:\big[from(1)\big]}\\\\\\\\\mapsto\tt{13+2M=23}\\\\\\\\\mapsto\tt{2M=23-13}\\\\\\\\\mapsto\tt{2M=10}\\\\\\\\\mapsto\tt{M=\cancel{\dfrac{10}{2} }}\\\\\\\\\mapsto\tt{\green{M=5\:km/hrs}}$

Putting the value of M in equation (1), we get;

$\mapsto\tt{R=13+5}\\\\\\\\\mapsto\tt{\green{R=18\:Km/hrs}}$

∴ The speed of the boat in still water is 18 km/hrs.

Answer 2

||✪✪ QUESTION ✪✪||

A boat can go 65 km upstream in 5 hrs. and 69 km downstream in 3 hrs. Find the speed of the boat in still water.

|| ★★ CONCEPT USED ★★ ||

if Speed of boat in x km/h , and speed of current is y km/h , Than :-

→ Speed in Downstream = (x + y) km/h .

→ Speed in Upstream = (x - y) km/h.

Also , Time = (Distance / Speed ) .

|| ✰✰ ANSWER ✰✰ ||

Let us assume That Speed of boat in Still water is x km/h , and speed of current is y km/h .

So, we can say That :-

→ 65/(x - y) = 5

→ (x - y) = 13 ---------- Equation (1).

________________

And,

→ 69/(x +y) = 3

→ (x + y) = 23 = ------------ Equation (2) .

_______________

Adding Equation (1) & (2) Now, we get,

→ (x - y) + (x + y) = 23 + 13

→ 2x = 36

Dividing both sides by 2 we get,

→ x = 18km/h.

Hence, we can say That, the speed of the boat in still water is 18km/h.