Question

Swati can row her boat at speed of 5 km /hr in still water . If it takens her 1 hr more to row the boat 5.25 km upstream than to return downstream. Find the speed of the stram.

Answer 1

Let the speed of the upstream be x km/hr

• Speed of the boat upstream = (5 - x) km/hr

• Speed of the boat downstream = (5 + x) km/hr

• Time taken for going upstream=$\sf\dfrac{5.25}{5 - x} \: hrs.$

• Time taken for going downstream=$\sf \dfrac{5.25}{5+x} \: hrs.$

Obviously, time taken for going 5.25 km upstream is more than the time taken for going 5.25 km downstream. But...it's given that the time taken for going 5.25 km. Upstream is 1 hr more than the time taken for going 5.25 downstream.

$\therefore \qquad \qquad \sf \dfrac{5.25}{5 - x} - \sf \dfrac{5.25}{5 + x} = 1$

$\implies \sf \sf5.25 \left \lbrace\dfrac{1}{5 - x} - \sf \dfrac{1}{5 + x} \right \rbrace= 1$

$\implies \sf \dfrac{21}{4} \left \lbrace \dfrac{5 + x - 5 + x}{(5 - x)(5 + x)} \right \rbrace = 1 \quad \: \: \because\left \lbrack \dfrac{21}{4} = 5.25 \right \rbrack$

$\implies \sf \dfrac{21}{{}_ {_{ \normalsize {2}}} \cancel{4}} \times \dfrac{ \cancel{2}x}{25 - {x}^{2} } = 1$

$\implies \sf \dfrac{21}{2} \times \dfrac{x}{25 - {x}^{2} } = 1$

$\implies \sf21x = 50 - {2x}^{2}$

$\implies \sf {2x}^{2} + 21x - 50= 0$

$\implies \sf {2x}^{2} + 25x - 4x- 50= 0$

$\implies \sf x(2x + 25) - 2(2x + 25) = 0$

$\implies \sf (2x + 25) (x- 2)= 0$

$\implies \begin{array}{l | l} \sf x - 2 = 0& \sf 2x + 25 \\ \qquad \sf x = 2 &\sf \: \: x ≠ -\dfrac{25}{2} \quad as \: x > 0\end{array}$

"Hence, the speed of the stream is 2 km/hr."

Answer 2

CONCEPT -:

• IN THESE QUESTION WE HAVE LEARN ABOUT
• Word Problems on Upstream/Downstream we have provided Swati can row her boat at speed of 5 km /hr 1 hr more to row the boat 5.25 km upstream

some information about Word Problems on Upstream/Downstream

• upstream means flow of river against the direction of moving of boat

• downstream means flow of river towards the direction of moving of boat

TIP -:

• Let the quantity as x and form a quadratic equation, then solve it.

EXPLANATION :

• Let the speed of stream is x km/hr, so total time taken to complete the journey in upstream and downstream will be,

5.25 / 5 - x = 5 .25 /5+ x + 1

5.25 (5 + x) = 5.25 (5 - x) + (5 + x) (5 − x)

x ^ 2 + 10.5x - 25 = 0

x ^ 2 + 12.5 x - 2x - 25 = 0

(x - 2)(x + 12.5) = 0

x = 2 or - 12.5 (speed can't be negative)

x = 2

FINAL ANSWER :

• The speed of stream is 2 km/hr.