Q.28. A motorboat whose speed is
18km/hr in still water takes 1 hour
more to go 24 km upstream than to
return downstream to the same spot
. Find the speed of the stream.
Answers
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
Explanation:
it take a lot of time please mark me the
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