Question

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

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Answer 1

Answer:

• The speed of the stream is 6 km/h.

Step-by-step explanation:

Given that:

• A motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream than to return downstream to the same spot.

To Find:

• The speed of the stream.

We know that:

• ✠ Time = Distance/Speed

Let us assume:

• The speed of the stream be x km/h.

• Time taken in upstream = 24/(18 - x)
• Time taken in downstream = 24/(18 + x)

Finding the speed of the stream:

According to the question.

⟶ 24/(18 - x) - 24/(18 + x) = 1

Taking 24 common in LHS.

⟶ 24{1/(18 - x) - 1/(18 + x)} = 1

⟶ 1/(18 - x) - 1/(18 + x) = 1/24

Taking (18 - x)(18 + x) as LCM in LHS.

⟶ (18 + x - 18 + x)/{(18 - x)(18 + x)} = 1/24

⟶ 2x/(324 - x²) = 1/24

Cross multiplication.

⟶ 2x × 24 = 324 - x²

⟶ 48x = 324 - x²

⟶ x² + 48x - 324 = 0

⟶ x² + 54x - 6x - 324 = 0

⟶ x(x + 54) - 6(x + 54) = 0

⟶ (x - 6) (x + 54) = 0

⟶ x = 6 or x = - 54

∴ The speed of the stream = 6 km/h [Speed can't be negative]

Answer 2

Answer:

Given :-

• A motorboat whose speed is still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot.

To Find :-

• What is the speed of the stream.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Time =\: \dfrac{Distance}{Speed}}}}$

Solution :-

Let, the speed of the stream be x kmph

According to the question :

$\implies \sf \dfrac{24}{18 - x} - \dfrac{24}{18 + x} =\: 1$

$\implies \sf \dfrac{24(18 + x) - 24(18 - x)}{(18 - x) (18 + x)} =\: 1$

$\implies \sf \dfrac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} =\: 1$

$\implies \sf \dfrac{24(2x)}{324 - {x}^{2}} =\: 1$

By doing cross multiplication we get :

$\implies \sf 324 - {x}^{2} =\: 24(2x)$

$\implies \sf 324 - {x}^{2} =\: 48x$

$\implies \sf - {x}^{2} - 48x + 324 =\: 0$

$\implies \sf {x}^{2} + 48x - 324 =\: 0$

$\implies \sf {x}^{2} - 6x + 54x - 324 =\: 0$

$\implies \sf x(x - 6) + 54(x - 6) =\: 0$

$\implies \sf (x + 54)(x - 6) =\: 0$

$\implies \sf x + 54 =\: 0$

$\rightarrow \sf\bold{\red{x =\: - 54}}$

Either,

$\implies \sf x - 6 =\: 0$

$\rightarrow \sf\bold{\red{x =\: 6}}$

We can't take speed as negative (- ve).

So, x = 6

$\therefore$ The speed of the stream is 6 kmph .