Respuesta :
The speed of motorboat is 36 kmph and speed of current is 4 kmph.
Step-by-step explanation:
Distance covered in 4 hours = 160 km
Time took on return trip = 5 hours
Let,
x represent the speed of boat.
y represent the speed of current.
Combined speed of boat and current when in same direction = x+y
Speed of boat and current when travelling against = x-y
Distance = Speed * Time
Speed = [tex]\frac{Distance}{Time}[/tex]
x+y = [tex]\frac{160}{4}[/tex]
x+y = 40 Eqn 1
x-y = [tex]\frac{160}{5}[/tex]
x-y = 32 Eqn 2
Adding Eqn 1 and Eqn 2
[tex](x+y)+(x-y)=40+32\\x+y+x-y=72\\2x=72[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{72}{2}\\x=36[/tex]
Putting x=36 in Eqn 1
[tex]36+y=40\\y=40-36\\y=4[/tex]
The speed of motorboat is 36 kmph and speed of current is 4 kmph.
Keywords: linear equation, addition
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The Speed of motor boat is [tex]36\;\rm{km/hr}[/tex] and speed of current is [tex]4\;\rm{km/hr}[/tex].
Given information:
A motorboat traveling with a current can go [tex]160\;\rm{km[/tex] in [tex]4[/tex] hours. Against the current, it takes [tex]5[/tex] hours to go the same distance.
Let the speed of boat be u and speed of current be v.
Combined speed of boat and current when in same direction, u+v
And Speed of boat and current when travelling against, u-v
Now, Using the relation of Distance, speed and time, [tex]\rm{distance}={speed}\times{time}[/tex]
In case1: The motorboat traveling with a current, then formulated this situation in equation form we get:
[tex]u+v=\frac{160}{4} \\u+v=40\;\;\;..........(1)[/tex]
In case 2: The motorboat traveling against the current, then formulated this situation in equation form we get:
[tex]u-v=\frac{160}{5}\\u-v=32\;\;\;\'............(2)[/tex]
Adding equation [tex](1)[/tex] and [tex](2)[/tex] we get:
[tex]u+v+u-v=40+32\\[/tex]
[tex]2u=72\\[/tex]
[tex]u=36[/tex]
Substituting the value of [tex]u=36[/tex] in equation [tex](1)[/tex] we get,
[tex]36+v=40[/tex]
[tex]v=4[/tex]
Therefore, Speed of motor boat is [tex]36\;\rm{km/hr}[/tex] and speed of current is [tex]4\;\rm{km/hr}[/tex].
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