# Question #52578

Mar 2, 2017

$S 1 = 110 \frac{m i}{h}$; $S 2 = 135 \frac{m i}{h}$

#### Explanation:

The speed of one of the planes can be defined as $S 1 \frac{m i}{h}$.

The speed of the second is then $S 2 = \left(S 1 + 25\right) \frac{m i}{h}$.

The planes are travelling in opposite directions and are moving away from each other at the speeds above over the given time.
That means we have to ADD the speed of the two planes to arrive at the rate at which they are travelling apart.

$r = S 1 + \left(S 1 + 25\right) = 2 S 1 + 25$

Here the distance is $490 m i$, and the time is $2 h$.

Distance traveled is defined as rate (speed) multiplied by time.

$d = r t$

$490 m i = \left(2 S 1 + 25\right) \frac{m i}{h} \times 2 h$

$490 = 4 S 1 + 50$

$4 S 1 = 490 - 50$

$4 S 1 = 440$

$S 1 = \frac{440}{4} = 110 \frac{m i}{h}$

$S 2 = \left(S 1 + 25\right) \frac{m i}{h} = 135 \frac{m i}{h}$