Question

Question #df8c1

Answer 1

The speed of the boat in still water is `18 mph`
The speed of the current is `9 mph`

Explanation:

If we use the equation`" rate" xx "time = distance"` and we simplify this using a system of equations for the boat travelling both upstream and downstream.

The rate for the boat downstream is a combination of the boat speed plus the current

`r_d =(s + c)`
`t_d = 7hrs`
`d_d = 189 mi`
`(s+c)7 = 189`

The rate for the boat upstream is a combination of the boat speed minus the current

`r_u =(s - c)`
`t_u = 21hrs`
`d_u = 189 mi`
`(s-c)21 = 189`

Set up the system of equations
`(s+c)7 = 189`
`(s-c)21 = 189`

Use the distributive property
`7s+7c = 189`
`21s-21c = 189`

Multiply the top equation by three as to cancel one of the variables
`3(7s+7c )= 189`
`21s-21c = 189`

`21s+21c = 567`
`21s-21c = 189`

Cancel and add the two equations
`21scancel(+21c) = 567`
`21scancel(-21c) = 189`

`42s = 756`

Divide by 42 on both sides to isolate the variable
`(cancel(42)s)/cancel(42) = 756/42`

`s=18` This is the speed of the boat in still water

To find the rate of the current, plug the boat speed into either of the original equations and solve for `c`

`7(18)+7c = 189`
`126 +7c =189`
`cancel126 +7c cancel(-126) =189-126`
`7c=63`

`c=9` This is the speed of the current

Answer 2

The boat travels at `18 mph` in still water.

The speed of the current is `9mph`

Explanation:

We know that distance travelled downstream is the same as the distance travelled upstream.

The time downstream is `7` hours and back upstream is `21` hours

`"Time" = "Distance"/"Speed"" "rArr "Speed" = "Distance"/"Time"`

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

The speed downstream is the speed of the boat PLUS the current.
The speed upstream is the speed of the boat MINUS the current.

Speed Downstream: `x+y = 189/7 = 27`

Speed Upstream: `" "x-y = 189/21 = 9`

Add the two equations together:

`2x = 36`

`x =18` miles per hour is the speed of the boat in still water.

`18+y = 27`

`y= 9` miles per hour is the speed of the current.

Check:
Downstream: Time `=189/27 = 7` hours

Upstream: Time `= 189/9= 21` hours