a motorboat whose speed is 18 kilometre per hour in still water takes 1 hour to go 24 km upstream then to return downstream to the same spot find the speed of the stream
Answers
Answer:
Give ,
speed of boat in still water = 18km/hr
let the speed of the stream be x km/hr
speed of the boat upstream = speed of the boat still in water-speed of the stream
since, speed of boat upstream= ( 18 - x ) km/hr
speed of the boat downstream = speed of the boat still in water + speed of the stream
since, speed of the boat downstream = ( 18 + x ) km/hr
Step-by-step explanation:
Time of upstream journey = Time of downstream journey + 1 hr
Therefore,
Distance covered upstream/ speed of the boat upstream = Distance covered downstream / speed of the boat downstream + 1 hr
> 24 km/ ( 18 - x ) km/hr = 24km/ ( 18+x) km/hr + 1hr
> 24/(18-x) - 24/(18+ x) = 1
> 432+24x - 432+24x/ (18-x) (18+x) = 1
> 48x= 342- x square
> x square+ 48x - 342 = 0
> x square+54x-6x-342 = 0
> x{ x+54 }-6x{ x+54 } = 0
> { x+54 } { x-6 } = 0
> x+54 = 0 or x-6 = 0
> x = -54 or x = 6
Therefore, x=6 ( speed of the stream cannot be negative)
Thus, the speed of the stream is 6 km/h.
Thanku
Hope the answer will help u !
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