a boat can move downwards at a speed of 16 km per hour and upstream at a speed of 9 km per hour what is the speed of the stream and the speed of the boat in still water
Answers
Step-by-step explanation:
Let the speed of boat is x km/hr and the speed of stream is y km/hr
Speed of boat in downstream = 16 km/hr
⇒ x + y = 16 ----(1)
Speed of boat in upstream = 10 km/hr
⇒ x - y = 10 ----(2)
From equation (1) and (2)
x = 13 and y = 3
∴ speed of boat in still water = 13 km/hr
Answer:
Let x be the speed of the stream.
⇒ Speed of the boat in still water is 8km/hr
⇒ The speed of the boat in upstream is 8−xkm/hr
⇒ The speed of the boat in downstream is 8+xkm/hr
⇒ The time taken by the boat to cover 15km=
8−x
15
hr
⇒ The time taken by the boat to cover 22km=
8+x
22
hr
According to the question,
⇒
8−x
15
+
8+x
22
=5
⇒ 15(8+x)+22(8−x)=5(8−x)(8+x)
⇒ 120+15x+176−22x=5(64−x
2
)
⇒ 296−7x=320−5x
2
⇒ 5x
2
−7x−24=0
⇒ 5x
2
−15x+8x−24=0
⇒ 5x(x−3)+8(x−3)=0
⇒ (x−3)(5x+8)=0
⇒ x−3=0 and 5x+8=0
⇒ x=3 and x=−
5
8
Speed cannot be negative.
∴ The speed of the stream is 3km/hr