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.

Answer 1

Answer:

s=6km/hr

Step-by-step explanation:

Given:

Speed of boat in still water = 18km/hr

Let speed of the stream = s

Speed of boat upstream = Speed of boat in still water - speed of stream = 18−s

Speed of boat down stream = Speed of boat in still water + speed of stream = 18+s

Time taken for upstream = Time taken to cover downstream + 1

24(18+s)=24(18−s)+(18−s)(18+s)

⇒s  

2

+48s−324=0

⇒s  

2

+54s−6s−324=0

⇒(s+54)(s−6)=0

⇒s=6,−54

⇒s



=−54

Thus, s=6km/hr, Speed of steam cannot be negative.

Answer 2

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Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

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

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

x2 + 48x - 324 = 0

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

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr