Question

A motorboat maintained a constant speed of 24 miles per hour relative to the water in going 45 miles upstream and then returning.The total time for the trip was 4.0 hours. Use this information to find the speed of the current.The speed of the curren is____________ miles per hour.

Answer 1

`\large \boxed{\text{6 mi/h}}`

Explanation:

Let s = speed of current

Then 24 - s = speed of motorboat upstream

and 24 + s = speed of motorboat downstream

Distance = speed × time

`\begin{array}{rcl}\text{Time} & = & \frac{\text{ distance}}{\text{speed}}\\\\4.0 & = & (45)/(24 - s) + (45)/(24 + s)\\\\4.0(24 + s)(24 - s) & = &45(24 + s) + 45(24 - s)\\4.0(576 - s^(2)) & = &1080+ 45s + 1080 - 45s\\576 - s^(2) & = & 2160\\576 - s^(2) & = & 540\\s^(2)& = &36\\s &=& \textbf{6 mi/h}\end{array}\\\text{The speed of the current is $\large \boxed{\textbf{6 mi/h}}$}`

Check:

`\begin{array}{rcl}4.0 & = & (45)/(24 - 6) + (45)/(24 + 6)\\\\4.0 & = & (45)/(18) + (45)/(30)\\\\4.0 & = & 2.5 + 1.5\\4.0 & = & 4.0\\\end{array}`

OK.