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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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
⇒
Speed
upstream
Distance
upstream
=
Speed
downstream
Distance
downstream
+1
⇒
18−s
24
=
18+s
24
+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.
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