a boat goes 36km downstream and 25 km upstream in 9 hours it can go 45km downstream and 35 km upstream in 12 hours. find the speed of boat in still water and that of stream
plz answer correctly with reference to ch 3 class 10 Cbese
Answers
Given:
In 9 hours: The boat goes 36 km downstream and 25 km upstream
In 12 hours: The boat goes 45 km downstream and 35 km upstream
To find:
The speed of the boat in still water.
Solution:
Let the speed of boat in still water= x km/hr
And speed of the stream = y km/hr
First case:
Speed of boat in downstream = x+y km/hr
Distance travelled by boat = 36 km
Since speed = distance/ time
time = 36/ (x+y) hr
Speed of boat in upstream= x-y km/hr
Distance travelled by boat = 25 km
Since speed = distance/ time
time = 25/ (x-y) hr
Total time = 9 hours= 36/ (x+y) hr+ 25/ (x-y) hr (1)
Second case:
Speed of boat in downstream = x+y km/hr
Distance travelled by boat = 45 km
Since speed = distance/ time
time = 45/ (x+y) hr
Speed of boat in upstream= x-y km/hr
Distance travelled by boat = 35 km
Since speed = distance/ time
Time = 35/ (x-y) hr
Total time = 12 hours= 45/ (x+y) hr+ 35/ (x-y) hr (2)
Let a= 1/ (x+y) and b=1/(x-y), then the equations 1 and 2 become:
36a + 25b = 9
45a + 35b = 12
On solving we get a= 1/9 = 1/(x+y)
And b= 1/5 = 1/(x-y)
We get x+y = 9 and x-y = 5
On solving we get: x = 7 and y = 2.
The speed of boat in still water is 7 km/hr.