Larry's time to travel 364 miles is 3 hours more than Terrell's time to travel 220 miles. Terrell drove 3 miles per hour faster than Larry. How fast did each one travel?

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Answer 1 · 2015-11-12T14:54:32

Terrell's speed $= 55$ $= 55$ mph
Larry's speed $= 52$ $= 52$ mph

Let $x$ $x$ be Larry's travel time.

$\Rightarrow$ $=>$ Terrell's travel time $= x - 3$ $= x - 3$

Let $y$ $y$ be Larry's speed

$\Rightarrow$ $=>$ Terrell's speed $= y + 3$ $= y + 3$

$x y = 364$ $xy = 364$

$\Rightarrow x = \frac{364}{y}$ $=> x = 364/y$

$(x - 3) (y + 3) = 220$ $(x - 3)(y + 3) = 220$

$\Rightarrow (\frac{364}{y} - 3) (y + 3) = 220$ $=> (364/y - 3)(y + 3) = 220$

$\Rightarrow (\frac{364 - 3 y}{y}) (y + 3) = 220$ $=> ((364 - 3y)/y)(y + 3) = 220$

$\Rightarrow (364 - 3 y) (y + 3) = 220 y$ $=> (364 - 3y)(y + 3) = 220y$

$\Rightarrow 364 y + 1092 - 3 y^{2} - 9 y = 220 y$ $=> 364y + 1092 - 3y^2 - 9y = 220y$

$\Rightarrow - 3 y^{2} + 355 y + 1092 - 220 y = 0$ $=> -3y^2+ 355y + 1092 - 220y = 0$

$\Rightarrow - 3 y^{2} + 135 y + 1092 = 0$ $=> -3y^2 + 135y + 1092 = 0$

$\Rightarrow y^{2} - 45 y + 364 = 0$ $=> y^2 - 45y + 364 = 0$

$\Rightarrow (y - 52) (y + 3) = 0$ $=> (y - 52)(y + 3) = 0$

$\Rightarrow y = 52, y = - 3$ $=> y = 52, y = -3$

But since we are talking about speed, the value should be positive

$\Rightarrow y = 52$ $=> y = 52$

$\Rightarrow y + 3 = 55$ $=> y + 3 = 55$