LE 26 A motorboat whose speed in still water is 24 km/hr, takes 1 hour
more to go 32 km upstream than to return downstream to the same
spot. Find the speed of the stream.
Answers
Answer:
Total Distance = 32km
Speed in Still Water = 24km/hr
Let the speed of stream be 'x' kmph
then, Speed moving upstream = 24-x
Speed moving downstream = 24+x
We know that is time
On reducing it to a quadratic equation,
we get - x^{2} + 64x-576=0x
2
+64x−576=0
On solving it by splitting the middle term method (8&72 as factors) we get,
x = 8 or -72
Since, the speed cannot be negative, x = 8
Therefore, the speed of the stream is 8 km/hr
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