Question 207393

Raffaele ran 8 miles and then walked 6 miles. If he ran 5 mph faster than he walked and the total time was 2 hours, then how fast did he walk?


Let Raffaele's walking rate of speed be S


Then his running rate of speed is S + 5 (he ran 5 mph faster than he walked)


{{{Time = distance/rate}}}


Since he ran 8 miles, walked 6 miles, and did them in 2 hours, then

{{{8/(S + 5) + 6/S = 2}}}

8(S) + 6(S + 5) = 2(S)(S + 5) [Multiplying equation by LCD, S(S + 5)]

{{{8S + 30 + 6S = 2S^2 + 10S}}}

{{{2S^2 - 4S - 30 = 0}}}

{{{2(S^2 - 2S - 15)= 0}}}

{{{S^2 - 2S - 15 = 0}}} Eliminate 2 = 0, as {{{2 <> 0}}}


(S - 5)(S + 3) = 0


S = 5, or - 3 (Eliminate S = -3, as rate of speed CANNOT be negative)


Therefore, Raffaele's walking rate of speed = {{{highlight_green(5)}}} mph