Question

A motorboat whose speed is 24km/hr in still water takes 1 hour more to go 32km upstream than to return downstream to the same spot find the speed of the stream​

Answer 1

$\huge \underline \mathsf \red {SOLUTION:-}$

Given That:

• Total Distance = 32km
• Speed in Still Water = 24km/h

ExPlanation:

Let the speed of the stream be ‘x’ km/h

then, Speed moving upstream = 24 - x

Speed moving downstream = 24 + x

Now for upstream journey

• Time taken = 32/24 - x hours

For downstream journey

• Time taken = 32/24 + x hours

Difference between timings =1 hr

Time of upstream journey = Time of downstream journey +1 hr

Hence,

The equation becomes:

(32/24 - x) - (32/24 + x) = 1

➠ 1/32 = (1/24 - x) - (1/24 + x)

➠1/32 = (24 + x - 24 + x) / 242- x²

➠ 242 - x² = 64x

➠ x² + 64x - 576 = 0

On factorising we get:

x² + 72x - 8x - 576 = 0

➠ x(x + 72) - 8 (x + 72) = 0

➠ (x - 8)(x = 72) = 0

➠ x = 8 or x = -72

Speed cannot be negative

• Hence x = 8

Therefore,

• The speed of the stream is 8 km/hr

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Answer 2

$\large\sf\underline{Answer:-}$

Total Distance = 32km

Speed in Still Water = 24km/h

ExPlanation:

Let the speed of the stream be ‘x’ km/h

then, Speed moving upstream = 24 - x

Speed moving downstream = 24 + x

Now for upstream journey

Time taken = 32/24 - x hours

For downstream journey

Time taken = 32/24 + x hours

Difference between timings =1 hr

Time of upstream journey = Time of downstream journey +1 hr

Hence,

The equation becomes:

• (32/24 - x) - (32/24 + x) = 1
• 1/32 = (1/24 - x) - (1/24 + x)
• 1/32 = (24 + x - 24 + x) / 242- x²
• 242 - x² = 64x
• x² + 64x - 576 = 0

On factorising we get:

• x² + 72x - 8x - 576 = 0
• x(x + 72) - 8 (x + 72) = 0
• (x - 8)(x = 72) = 0
• x = 8 or x = -72

Speed cannot be negative

Hence x = 8

Therefore,

The speed of the stream is 8 km/hr