A boat take 6 hours to travel 36 km downstream and 24 km upstream it takes 9 hours to travel 48 km downstream and 40 km upstream find the speed of the stream and that of boat in still water
Answers
Total Time =
Upstream distance/upstream speed + Downstream dist/downstream speed
Let speed of boat=x
Let speed of stream=y
Upstream speed = speed of boat - speed of stream = x - y
Down stream speed = speed of boat + speed of stream = x + y
Given 36/x+y + 24/x-y = 6 hours...... (i)
48/x+y + 40/x-y = 9 hours.......(ii)
Multiply eq.(i) by '5' and eq.(ii) by '3'
180/x+y + 120/x-y = 30.....(iii)
144/x+y + 120/x-y = 27.....(iv)
Subtract above equations:
36/x+y = 3
x+y = 12.....(a)
(a) in (iv)
144/12 + 120/x-y = 27
12 + 120/x-y = 27
120/x-y = 15
x-y = 8
x+y = 12
Adding both:
2x = 20
x=10
10+y = 12
y=2
Speed of boat in still water = 10 kmph
Speed of stream = 2 kmph
Hope this helps
Answer:
speed of the boat in still water is 10 km/h and speed of stream is 2 km/h
Step-by-step explanation:
this can be done by using references from the topic of linear equations in 2 variables
speed of boat in still water = x
stream = y
time taken to go up as well as down = 6 hours
t1 +t2 = 6 hours
t1 = (36/x+y)
t2 = (24/x-y)
form the equations
2nd part
upstream + downstream = 9 hours
t3 + t4 = 9
t3 = (48/x + y)
t4 = (40/x-y)
solve the two pairs of equation with reduction method
you will finally get
x+y = 12
x-y = 8
2x = 20
x= 10
y = 2
this is my first answer please convey whether its helpful or not
:)