Question

a motor boat whose speed is 18 km/h in still water takes one hour to go 24km up steam than to return down steam to the same spot Find the speed of the steam

Answer 1

Answer:

Given parameters:

The speed of the motorboat in still water =18 kmph

Let us consider

The speed of the stream = s

Speed of boat upstream = Speed of a boat in still water – the speed of a stream

Speed of boat upstream = 18 – s

Speed of boat downstream = Speed of a boat in still water + speed of a stream

Speed of boat downstream = 18 + s

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

time =distance/speed

DistanceupstreamSpeedupstream=DistancedownstreamSpeeddownstream+1

24/ (18 – s) = [24/(18 + s)] + 1

24(18+s) = 24(18−s) + (18−s)(18+s)

s2 + 48s − 324 = 0

s2 + 54s − 6s − 324 = 0

(s+54)(s−6) = 0

s = 6,−54 but

s ≠−54

Since the speed of steam cannot be negative.

∴ s = 6km/hr

Answer 2

Step-by-step explanation:

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

⇒ Distance upstream/speed upstream= Distance downstream/speed downstream + 1

⇒ 24/18-s= 24/18+s +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.