Question

A sailor goes 8km downstream in 40 min. and comes back in 1 hr. Determine the speed of the sailor in the still water and the speed of the current.

Answer 1

speed of the stream = 2 km/hr
let speed of the boat in still water be x km/hr

Time taken to travel downstream = 8/(x+2)
Time taken to travel upstream = 8/(x-2)

Total time = 1 hr 40 min = 5/3 hr
8(x+2)+8(x−2)=538(x+2)+8(x−2)=53

24(x- 2) + 24(x+2)  = 5(x+2)(x-2)
48x = 5x2 - 20
5x2 - 48x -20=0

x =  48±√(−48)2−4×5×(−20)2×548±(−48)2−4×5×(−20)2×5

=48±√2304+40010=48±2304+40010  

=48±5210=48±5210 

= 10 (taking only the positive value)

i.e., speed of the boat in still water = 10 km/hr  (0)  (0) Comment 
1 year ago,  Raj (Senior Maths Expert, careerbless.com)let speed in still water = xspeed upstream =x-2downstream speed=x+2
8/(x+2)+8/(x-2)=5/3 hrs
solving this we get x=10, -2/5, since speed cant be negative, answer is 10

Answer 2

Answer:

⇒ x + y = 12  

⇒ x - y = 8  

--------------  

⇒ 2x = 20,  

⇒ 2y = 4  

⇒ x = 10,  

⇒ y = 2  

⇒Speed of stream = 2 kmph, Speed of boat = 10 kmph