To answer this item, we let x be the speed of the boat in
still water. The speed of the current, we represent as y.
When the boat travels upstream or against the current,
the speed is equal to x – y and x + y if it travels downstream or along with
the current.
The time it takes for the an object to travel a certain
distance is calculated by dividing the distance by the speed.
First Travel: 35
/ (x – y) + 55 / (x + y) = 12
Second travel: 30 / (x – y) + 44 / (x + y) = 10
Let us multiply the two equations with the (x-y)(x+y)
This will give us,
35(x
+ y) + 55(x – y) = 12(x-y)(x+y)
30(x
+ y) + 44(x – y) = 10(x-y)(x+y)
Using dummy variables:
Let a = x + y and b be x – y
35a
+ 55b = 12ab
30a
+ 44b = 10ab
From the first equation,
b = 35a/(12a – 55)
Substituting to the second equation,
30a
+ 44(35a/(12a – 55)) = 10a(35a/(12a-55))
The value of a is 11.
b = 35(11)/(12(11) – 55))
b = 5
Putting back the equations,
x + y = 11
x – y = 5
Adding up the equations give us,
2x = 16
<em> x = 8
km/hr</em>
The value of x, the speed of the boat in still water, is
8 km/hr.
