Question

Hø|á!!

A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

➡ Class 10
➡ CH - 3
➡ Linear equations in two variables

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Answer 1

A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Good question,

Here is your answer!

Let the speed of stream be v.

Speed of boat in downstream = (18 + v),

Speed of boat in upstream = (18 - v).

According to question,

t(up) - t(d) = 1 hr

t refers to time here.

time = distance /speed,

=) 24/(18 - v) - 24/(18+v) = 1

=) 24[1/18-v - 1/18+v] = 1

=) 24[(18+v)-(18-v)]/18² - v² = 1

=) 24(2v) = 324 - v²

=) v² + 48v - 324 = 0

=) v² +54v - 6v - 324 =0

=) v(v + 54) - 6(v+54) = 0

=) (v-6) (v+54) =0

Hence v-6 = 0

=) v = 6km/hr.

Answer 2

▶ Error:-

→ This question is of chapter - 4 ; Quadratic equations .


▶ Question :-

→ A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.



▶ Answer :-

→ 6 km/hr .



▶ Step-by-step explanation :-

→ Speed of the motorboat in still water = 18 km/hr .

→ Let the speed of the stream be x km/hr .

→ Then, speed upstream = ( 18 - x ) km/hr .

→ Speed downstream = ( 18 + x ) km/hr .

→ Time taken to go 24 km upstream = $\frac{24}{(18-x)}$ hours .

→ Time taken to return 24 km downstream = $\frac{24}{(18+x)}$ hours .



$\huge \pink{ \mid \underline{ \overline{ \tt Solution :- }} \mid}$


$\sf \because \frac{24}{(18 - x)} - \frac{24}{(18 + x)} = 1. \\ \\ \sf \implies \frac{1}{(18 - x)} - \frac{1}{(18 + x)} = \frac{1}{24} . \\ \\ \sf \implies \frac{(18 + x) - (18 - x)}{(18 - x)(18 + x)} = \frac{1}{24} . \\ \\ \sf \implies \frac{2x}{(324 - {x}^{2}) } = \frac{1}{24} . \\ \\ \sf \implies324 - {x}^{2} = 48x. \\ \\ \sf \implies {x}^{2} + 48x - 324 = 0. \\ \\ \sf \implies {x}^{2} + 54x - 6x - 324 = 0. \\ \\ \sf \implies x(x + 54) - 6(x + 54) = 0. \\ \\ \sf \implies(x - 6)(x + 54) = 0. \\ \\ \sf \implies x - 6 = 0. \: \: \green{or} \: \: x + 54 = 0. \\ \\ \sf \implies x = 6 \: \: \green{or} \: \: x = - 54. \\ \\ \huge{ \orange{ \boxed{ \boxed{ \tt \therefore x = 6.}}}} \\ \\ \bigg( \tt \because speed \: of \: the \: stream \: cannot \: be \: negative. \bigg)$



✔✔ Hence, the speed of the stream is 6 km/hr ✅✅ .




$\huge \blue{ \boxed{ \boxed{ \mathscr{THANKS}}}}$