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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Answers
Solution :
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Given :
The speed of the motor bike instill water is 18 kmph,
It takes 1 hour to travel upstream & return to same spot,.
From this information we can say that,
⇒ The speed of motor boat (boat's engine) = 18 kmph ,
⇒ It traveled 24 km upstream & 24km downstream in 1 hour,.
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To Find :
The speed of stream .
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We know that,
time = {distance}{speed}
speed
distance
So,
Let the speed of stream be x,
Then,
we can say that,
⇒ {24}{18 - x} - {18 + x} = 1
18−x
24
−
18+x
24
=1 .(i) (All the units are in hour km per hour,etc,.)
⇒ {24(18 + x)-24(18 - x)}{(18 - x)(18 + x)} = 1
(18−x)(18+x)
24(18+x)−24(18−x)
=1
⇒ {24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1
(18−x)(18+x)
24(18+x−18+x)
=1
⇒{24(2x)}{324 - x^2} = 1
324−x
2
24(2x)
=1
⇒ 324 - x^2 = 48x324−x 2
=48x
⇒ -x² - 48x + 324 = 0
⇒ x² + 48x - 324 = 0
⇒ x² - 6x + 54x - 324 = 0
⇒ x (x -6) + 54(x - 6) = 0
⇒ (x + 54)(x - 6) = 0
For the equation to be 0,
Either,
⇒ x + 54 = 0 (or) x - 6 = 0
⇒ x = -54 (or) x = 6
⇒ x = 6 (As speed can't be negative, x ≠ -54)
∴ The speed of the stream is 6 kmph
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Hope it Helps!!
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
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