A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Answers
EXPLANATION.
To find the speed of stream.
According to the question,
Speed of boat in still water = x km/hr
Let the speed of stream = s
speed of boat upstream =
speed of boat in still water - speed of stream
=> 18 - s .......(1)
speed of boat downstream =
speed of boat in still water + speed of stream
=> 18 + s .......(2)
Time taken to upstream = time taken
to downstream + 1
=> we get,
=> s² + 48s - 324 = 0
=> s² + 54s - 6s - 324 = 0
=> s ( s + 54 ) - 6 ( s + 54 ) = 0
=> ( s - 6 ) ( s + 54 ) = 0
=> s = 6 and s = -54
=> s ≠ -54
Therefore,
speed of stream = 6 km/hr
Step-by-step explanation:
Assume that the speed of the stream be x km/hr
A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot.
During upstream = (18 - x)
During downstream = (18 + x)
As per given condition,
→ 24/(18 - x) - 24(18 + x) = 1
→ 24[(18 + x) - (18 - x)]/[(18 - x)(18 + x)] = 1
→ x² + 48x - 324 = 0
Split the middle term
→ x² + 54x - 6x - 324 = 0
→ x(x + 54) - 6(x + 54) = 0
→ (x - 6)(x + 54) = 0
→ x = 6, -54
Speed can't be negative. So, negative one neglected.
Hence, the speed of the stream is 6 km/hr