# word problem concerning speed

A man rows across a river 1/2 mi. wide and lands at a point 1/4 mi. farther down the river. If the banks of the river are parallel straight lines and he takes 1/2 h. to cross, what is his average speed in feet per minute if his course is a straight line?

I found 88 ft/min

• So what's the question? – bakula Nov 6 '15 at 21:18
• It's asking for the average speed. – user108343 Nov 6 '15 at 21:20
• Yes, but what is $\textit{your}$ question? Do you just want somebody to check your answer? – bakula Nov 6 '15 at 21:21
• Yeah this is what I want – user108343 Nov 6 '15 at 21:28

Consider a right triangle having legs $1/2~\mathrm{mile}$ & $1/4~\mathrm{mile}$ then the man will follow the straight line path along the hypotenuse given as $$=\sqrt{\left(\frac{1}{2}\right)^2+\left(\frac{1}{4}\right)^2}=\frac{\sqrt 5}{4}\ ~\mathrm{miles}=\frac{5280\sqrt 5}{4}=1320\sqrt 5\ ~\mathrm{ft}$$ hence, the average speed of the man $$=\frac{\text{distance traveled}}{\text{time taken}}=\frac{1320\sqrt 5~\mathrm{ft}}{30~\mathrm{min}}=\color{red}{44\sqrt 5\approx 98.387 ~\mathrm{ft/min}}$$