Question

The speed of a motorboat is 16 km/hr in still water. It goes 21 km upstream and then returns downstream to the initial position in 3 hours. Find the speed of the stream.​

Answer 1

let speed of stream be x

21 = (16+x)/3-a

21 = (16-x)/3-a

2 eqn 2 unknown

solve and get the answer

pls mark as brainliest

Answer 2

Let the speed of the stream be x Km/hr

Speed of boat in still water = 16 Km/hr

Speed of a boat (Downstream) = (16+x) Km/hr

Speed of a boat (Upstream) = (16-x) Km/hr

• Upstream means against the direction of stream ; Downstream means in the direction of stream.

Distance travelled = 21 Km (in both case)

Time Taken (Upstream) = 21/(16-x) [T = D/V]

Time Taken (Downstream) = 21/(16+x)

Total time taken = 3 hours

$\sf \dfrac{21}{16 + x} + \dfrac{21}{16 - x} = 3$

$\rm \dfrac{ 21(16 - x) + 21(16 + x)}{{16}^{2} - {x}^{2}} = 3$

$\sf \dfrac{336 - 21x + 336 + 21x}{256 - {x}^{2} } = 3$

'21x' will be cancelled out

$\sf3 {x}^{2} = 768 - 672$

$\sf {x}^{2} = 32$

$\sf \: x = 4 \sqrt{2}$

Speed of stream = $\sf \: x = 4 \sqrt{2}$ Km/hr