Question

25. A boat travels 30 km upstream in the same amount of time it takes to travel 60 km
downstream in the same river. If the speed of the river is 4 km/h, find the speed of the
boat in still water.​

Answer 1

$\huge\underline\green{\sf Answer:-}$

★$\large{\boxed{\sf Speed\:Of\:boat=12m/s}}$

$\huge\underline\green{\sf Solution:-}$

★Given :-

Upstream = 30km

Downstream=60km

Speed of river (y) = 4 km/h

Speed of boat (x) = ?

We know that

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

Given time (t) is same for Upstream and Downstream

So ,

$\large{\sf {\frac{30}{x-y}}={\frac{60}{x+y}}}$

$\large{\sf 30(x+y)=60(x-y)}$

$\large{\sf 30x+30y=60x-60y}$

$\large{\sf 30x-60x =60x-30y}$

y = 4 m/s (given)

$\large{\sf -30x =-90×4}$

$\large{\sf x ={\frac{-90×4}{30}}}$

★$\large\red{\boxed{\sf Speed\:of\:boat(x) =12m/s}}$

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\red{Answer:-}}}}}$

${\bold{\underline{\underline{Given:-}}}}$

•Upstream= 30km

•Downstream= 60km

•Speed of river = 4km/h

${\bold{\underline{\underline{To \: find :-}}}}$

•speed of boat = ❓

${\bold{\underline{\underline{ Step-by-step-Explanation:-}}}}$

➡let the speed of boat be x km/h

➡let the speed of river be y km/h

Now ,we know that

$\huge\ Time = \frac{Distance}{Speed}$

So ,

➡For upstream ;

$\huge\implies\frac {30}{x-y}$

➡For Downstream;

$\huge\implies\frac {60}{x+y}$

Now,

$\huge\implies\frac {30}{x-y} = \frac {60}{x+y}$

$\implies\ 30(x+y)= 60(x-y) \\ \\ \implies\ 30x +30y = 60x -60y \\ \\implies \ -30x=90y (eq1) \\ \\ \implies\ y= 4m/s$

Putting value of y =4 in eq1

$\implies\ -30x=90y \\ \\ \implies\ x= \frac {-90 X 4 }{30} \\ \\ \implies\ x=12m/s$

✏$\large\pink{\boxed{\sf Speed of boat =12m/s}}$