Question

A cabin cruiser traveling with the current went 12 mi in 1 h. Traveling against the current it took 2 h to go the same distance. Find the rate of the cabin cruiser in calm water and the rate of the current.

Answer 1

in calm water 9mph

current rate 3mph

Explanation:

Answer 2

• Rate of the cabin cruiser in calm water:
  `9\; \rm mph`.
• Rate of the current:
  `3\; \rm mph`.

Explanation:

• Let the speed of the cruiser in calm water be
  `x\; \rm mph`.
• Let the speed of the current be
  `y\; \rm mph`.

The speed of the cruiser in the direction of the current would be
`(x + y) \; \rm mph`. Since the ship travels
`12\; \rm mi` at that speed in
`1\; \rm h`,
`1 * (x + y) = 12`.

The speed of the cruiser in the opposite direction of the current would be
`(x - y) \; \rm m \cdot s^(-1)`. Since the ship travels
`12 \; \rm mi` at that speed in
`2\; \rm h`,
`2 * (x - y) = 12`.

Hence the system of equations:

`\displaystyle \begin{cases}x + y = 12 \\ 2(x - y) = 12 \end{cases}`.

Divide both sides of the second equation by
`2` to obtain:

`x - y = 6`.

Add that to the first equation:

`2\; x = 18`.

Hence
`x = 9`.

Calculate
`y` using the first equation:

`y = 12 - x = 12 - 9 = 3`.

Hence:

• Rate of the cabin cruiser in calm water:
  `9\; \rm mph`.
• Rate of the current:
  `3\; \rm mph`.