Question

Please make this simple and easy, and help me quickly, thank you!

Answer 1

Given:

Total distance = 60 km

Upstream time = 5 hours

Downstream time = 3 hours

Find-:

The rate of boat in still water.

Explanation-:

Let

The speed of the boat in still water is"x"

The speed of the water is "y"

For upstream ( Against the current )

Speed of boat is:

`=x-y`
`\begin{gathered} \text{ Distance }=60\text{ km} \\ \\ \text{ Time }=5\text{ hours} \end{gathered}`

Use the formula:

`\text{ Speed}=\frac{\text{ Distance}}{\text{ Time}}`

For upstream speed is:

`\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x-y=(60)/(5) \\ \\ x-y=12..............(1) \end{gathered}`

For downstream,

`\text{ Speed}=x+y`
`\begin{gathered} \text{ Distance}=60\text{ km} \\ \\ \text{ Time}=3\text{ hours} \end{gathered}`

Use the formula of distance

`\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x+y=(60)/(3) \\ \\ x+y=20 \\ \\ y=20-x................(2) \end{gathered}`

From eq(2) put the value of "y" in eq(1) then the value is:

`\begin{gathered} x-y=12...........(1) \\ \\ y=20-x...............(2) \end{gathered}`
`\begin{gathered} x-y=12 \\ \\ x-(20-x)=12 \\ \\ x-20+x=12 \\ \\ 2x-20=12 \\ \\ 2x=12+20 \\ \\ 2x=32 \\ \\ x=(32)/(2) \\ \\ x=16 \end{gathered}`

The rate of the boat in still water is 16 km/hour