36. A sailor can row a boat 8 km downstream and
return back to the starting point in 1 hour 40
minutes. If the speed of the stream is 2 km per
hour, find the speed of the boat in still water.
Answers
Answer:
Speed of the stream =2 km/hr
Let speed of the boat in still water be x km/hr.
Time taken to travel downstream =
x+2
8
Time taken to travel upstream =
x−2
8
Total time =1 hr. 40 min =
3
5
hr.
Therefore,
x+2
8
+
x−2
8
=
3
5
⇒3(8x−16+8x+16)=5(x
2
−4)
⇒24x+24x=5x
2
−20
⇒5x
2
−48x−20=0
⇒5x
2
−50x+2x−20=0
⇒5x(x−10)+2(x−10)=0
⇒(x−10)(5x−2)=0
⇒x=10,
5
2
As speed cannot be in fraction, x=10 is the correct value.
Thus, speed of boat in still water is 10 km/h
Answer:
Step-by-step explanation:
Solution :
Let the speed of the boat in still water be x km/hr.
Speed of the stream = 2 km/hr.
∴ speed downstream=(x+2)kmhr,
speed upstream =(x−2)kmhr.
Time taken to cover 8 km downstream and return back to the starting point =8(x+2)+8(x−2). But, this time is given as 14060
hours =123 hours =53 hours.
∴ 8x+2+8x−2=53
⇒ 1x+2+1x−2=524⇒(x−2)+(x+2)(x+2)(x−2)=524
⇒ 2x(x2−4)=524⇒5x2−20=48x
⇒ 5x2−48x−20=0⇒5x2−50x+2x−20=0
⇒ 5x(x−10)+2(x−10)=0⇒(x−10)(5x+2)=0
⇒ x−10=0 or 5x+2=0
⇒ x=10 or x=−25
⇒ x=10 [∵ speed of the boat cannot be negative]
Hence, the speed of the boat in still water is 10 km/hr.
