Question

A motorboat maintained a constant speed of 1111 miles per hour relative to the water in going 1818 miles upstream and then returning. The total time for the trip was 5.55.5 hours. Use this information to find the speed of the current.

Answer 1

The speed of the current is 7 miles per hour.

Explanation:

Let x represent speed of the current.

We have been given that a motorboat maintained a constant speed of 11 miles per hour relative to the water in going 18 miles upstream and then returning.

The speed of motorboat while going upstream would be
`11-x`.

The speed of motorboat while going downstream would be
`11+x`.

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

Time taken while going upstream would be
`(18)/(11-x)`.

Time taken while going downstream would be
`(18)/(11+x)`.

Now we will compare sum of both times with total time 5.5 hours and solve for x as:

`(18)/(11-x)+(18)/(11+x)=5.5`

`(18(11+x))/((11-x)(11+x))+(18(11-x))/((11-x)(11+x))=5.5(11-x)(11+x)`

`198+18x+198-18x=5.5(11-x)(11+x)`

`396=5.5(121-x^2)`

`396=665.5-5.5x^2`

`665.5-5.5x^2=396`

`665.5-665.5-5.5x^2=396-665.5`

`-5.5x^2=-269.5`

`(-5.5x^2)/(-5.5)=(-269.5)/(-5.5)`

`x^2=49`

Take positive square root of both sides:

`√(x^2)=√(49)`

`x=7`

Therefore, the speed of the current is 7 miles per hour.