# 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?

##### 1 Answer
Nov 12, 2015

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

#### Explanation:

Let $x$ be Larry's travel time.

$\implies$Terrell's travel time $= x - 3$

Let $y$ be Larry's speed

$\implies$Terrell's speed $= y + 3$

$x y = 364$

$\implies x = \frac{364}{y}$

$\left(x - 3\right) \left(y + 3\right) = 220$

$\implies \left(\frac{364}{y} - 3\right) \left(y + 3\right) = 220$

$\implies \left(\frac{364 - 3 y}{y}\right) \left(y + 3\right) = 220$

$\implies \left(364 - 3 y\right) \left(y + 3\right) = 220 y$

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

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

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

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

$\implies \left(y - 52\right) \left(y + 3\right) = 0$

$\implies y = 52 , y = - 3$

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

$\implies y = 52$

$\implies y + 3 = 55$