Question

A motorboat goes downstream in the river and covers the distance between two coastal town in 3 hours. It covers this distance upstream in 4 hours. If the speed of the stream is 5 km/hr, find the speed of the boat in still water qnd the distance between the two coastal towns​

Answer 1

Answer:

Step-by-step explanation:

Since we have to find the speed of the boat in still water, let us suppose that it is x km/h.

This means that while going downstream the speed of the boat will be (x+2) kmph because the water current is pushing the boat at 2 kmph in addition to its own speed 'x' kmph.

Now the speed of the boat down stream =(x+2) kmph

⇒ distance covered in 1 hour =x+2 km

∴ distance covered in 5 hours =5(x+2) km

Hence the distance between A and B is 5(x+2)km

But while going upstream the boat has to work against the water current.

Therefore its speed upstream will be (x−2) kmph.

⇒ Distance covered in 1 hour =(x−2) km

Distance covered in 6 hours =6(x−2) km

∴ distance between A and B is 6(x−2) km

But the distance between A and B is fixed

∴ 5(x+2)=6(x−2)

⇒ 5x+10=−12−10

∴ −x=−22

x=22

Therefore speed of the boat in still water is 22 kmph.

Answer 2

$\sf \: Let \: the \: speed \: be \: x \: km/h.$

$\sf \: the \: speed \: while \: going \: downstream = (x+2) km {h}^{ - 1} \\ \sf \: (due \: to \: the \: water \: current \: pushing \: the \: boat)$

$\sf \: ⇒ distance \: covered \: in \: 1 \: hour =x+2 km$

$\sf \: ∴ distance \: covered \: in \: 3 \: hours = 3(x+2) km$

$\sf \: Hence,$

$\sf \: the \: distance \: between \: A \: and \: B = 3(x+2) \: km$

Now, while going upstream the boat has to work against the water current.

$\sf \therefore \: its \: speed \: upstream \: = (x−2) km {h}^{ - 1}$

$\sf \: ⇒ distance \: covered \: in \: 1 \: hour =(x−2) \: km$

$\sf \: distance \: covered \: in \: 4 \: hours \: = 4(x−2) km$

$\sf \: ∴ distance \: between \: A \: and \: B = 4(x−2) km$

$\sf \: ∴ 3(x+2) = 4(x−2) \\ \sf \implies \: 3x + 6 = 4x - 8 \\ \sf \implies \: 3x - 4x = - 8 - 6 \\ \sf \implies \: \cancel- x = \cancel- 14 \\ \sf x = 14.$

Therefore speed of the boat in still water is 14 km/h.