Question

A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours.

The speed of the boat in still water is ______ miles per hour.


The speed of the current is ______ miles per hour.

Answer 1

Explanation:

Answer 2

• The speed of the boat in still water is 8 miles per hour.

• The speed of the current is 4 miles per hour.

Solution:

We know the distance formula,

`Distance=(speed)/(time)`

`\Rightarrow Speed=Distance* Time`

As boat travelled 240 miles downstream in 20 hours,

speed=
`(240)/(20) =12` miles per hour.

As boat travelled 240 miles upstream in 60 hours,

speed=
`(240)/(60) = 4` miles per hour.

Let the speed of boat in still water be x and the speed of current be y.

So, the equations formed are:
`x+y=12`(downstream) --- (a) and
`x-y=4`(upstream). --- (b)

On solving, (a)

`\Rightarrow x=12-y` --- (c)

Substituting (c) in (b), we get
`12-y-y=4`

`\Rightarrow 12-2y=4 \Rightarrow 12-4=2y \Rightarrow 8=2y \Rightarrow (8)/(2)=y`

Therefore, y=4 --- (d)

On substituting (d) in (a) we get,

`x+4=12 \Rightarrow x=12-4 \Rightarrow x=8`

Therefore, x=8

Hence, Speed of boat in still water= 8 miles per hour and speed of current is 4 miles per hour.