The distance between two points is 48 km.A boat whose speed is 9 kmph in still water takes 4 hours less to travel downstream than upstream.What must be the speed of the boat in still water so that it can row downstream 75 km in 5 hours
Answers
Answer:
12 kmph
Explanation: y be speed of water
t be time
48/(9+y)=t-4
48/9-y=t (sub in above)
By solving we get y=3 kmph
Let x be speed of down stream new
75/5=x+3
So that x=12 kmph
The speed of the boat in still water so that it can row downstream 75 km in 5 hours is 12km/hr
Let the speed of water current be x km/hr.
Given that the speed of boat in still water is 9 km/hr.
Speed of boat downstream would be (9+x) km/hr
Again, speed of boat upstream would be (9-x) km/hr.
Time taken upstream = Distance/Speed = 48/(9-x)
Time taken downstream = Distance/Speed = 48/(9+x)
Given, difference in time = 4hrs. So,
48/(9-x) - 48/(9+x) = 4
⇒ 4[(9-x)(9+x)] = 48(9+x) - 48(9-x)
⇒ [(9-x)(9+x)] = 12(9+x) - 12(9-x) [Dividing both sides by 4]
⇒ (81-x²) = 2(12x) = 24x
⇒ x² + 24x - 81 = 0
⇒ x² + 27x - 3x - 81 = 0
⇒ x(x+27) -3(x+27) = 0
⇒ (x+27)(x-3) = 0
By zero product rule, we get:
x = - 27, which we cannot accept as speed cant be negative.
x = 3 km/hr, which is the speed of water current.
Let speed of boat in still water be y km/hr.
Speed of boat (S) in downstream = (y+3) km/hr
Distance to cover (D) = 75km.
Time taken (T) = 5hrs.
We know, S = D/T
So, (y+3) = 75/5 = 15
Thus, y = 15-3 =12km/hr, which is the speed of boat in still water.