Question

Victoria's speedboat can travel 105 miles upstream against a 4-mph current in the same amount of time it travels 125 miles downstream with a 4-mph current. Find the speed of Victoria's boat.

Answer 1

Recall that:

`\text{ time }=\frac{\text{ distance}}{\text{ speed}}`

Let Victoria's speed be v.

Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.

Hence the time of journey upstream is given by:

`(105)/(v-4)`

And the time of journey downstream is given by:

`(125)/(v+4)`

Since the time of journey upstream is the same as the time of journey downstream, it follows that:

`\begin{gathered} (105)/(v-4)=(125)/(v+4) \\ \text{ Divide both sides by }5: \\ (21)/(v-4)=(25)/(v+4) \\ \text{ Cross-multiplying, we have:} \\ 21(v+4)=25(v-4) \\ \text{ Expanding the expressions, we have:} \\ 21v+84=25v-100 \\ 25v-21v=100+84 \\ 4v=184 \\ v=(184)/(4)=46 \end{gathered}`

Therefore, Victoria's speed is 46 mph