Question

A boat takes twice as long to travel 5 km upstream as it does travel 3km downstream in a river that flows at a rate of 2 kph. At what speed does the boat travel in still water?

Answer 1

Explanation:

Explanation:

distance (d) = rate (r) x time (t)

UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t

DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t

*x is the speed in still water and y is the current of the water.

Upstream equation: 5 = 2t(x - 2) --> \dfrac{5}{2(x-2)}=t

2(x−2)

5

=t

Downstream equation: 3 = t(x + 2) --> \dfrac{3}{x+2}=t

x+2

3

=t

Set the equations equal to each other to solve for x:

\begin{gathered}\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x\end{gathered}

2(x−2)

5

=

x+2

3

Cross multiply:

5(x+2)=3⋅2(x−2)

Distribute:

5x+10=6x−12

Isolate x:

10=x−12

22=x

Answer 2

Answer: 22 kph

Explanation:

distance (d) = rate (r) x time (t)

UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t

DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t

*x is the speed in still water and y is the current of the water.

Upstream equation: 5 = 2t(x - 2) -->
`(5)/(2(x-2))=t`

Downstream equation: 3 = t(x + 2) -->
`(3)/(x+2)=t`

Set the equations equal to each other to solve for x:

`(5)/(2(x-2))=(3)/(x+2)\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x`