a motorboat traveling with a current can go 160km in 4 hours. against the current it takes 5 hours to go the same distance. find

Question

3 years ago

10

the speed of motorboat and speed of current

1 answer:

irakobra [83] · Answer 1 · 2022-06-09T18:39:09+03:00

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 = $\frac{Distance}{Time}$

x+y = $\frac{160}{4}$

x+y = 40 Eqn 1

x-y = $\frac{160}{5}$

x-y = 32 Eqn 2

Adding Eqn 1 and Eqn 2

$(x+y)+(x-y)=40+32\\x+y+x-y=72\\2x=72$

Dividing both sides by 2

$\frac{2x}{2}=\frac{72}{2}\\x=36$

Putting x=36 in Eqn 1

$36+y=40\\y=40-36\\y=4$

The speed of motorboat is 36 kmph and speed of current is 4 kmph.

Keywords: linear equation, addition

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