# Two planes leave from Topeka, Kansas. The first plane travels east at a rate of 278 mph. The second plane travels west at a speed of 310 mph. How long will it take for them to be 1176 miles apart?

Feb 17, 2017

Extreme detail given. With practice you would become much faster than this using shortcuts.

the plains would be 1176 miles apart at 2 hours flight time

#### Explanation:

Assumption: both planes are traveling in a strait line and they take off at the same time.

Let time in hours be $t$

The speed of separation is $\left(278 + 310\right) m p h = 588 m p h$

Distance is speed (velocity) multiplied by time.

$588 t = 1176$

Divide both sides by 588

$588 t \div 588 = 1176 \div 588$

$\frac{588}{588} \times t = \frac{1176}{588}$

But $\frac{588}{588} = 1$

$1 \times t = \frac{1176}{588}$

$t = \frac{1176}{588}$

$t = 2 \text{ hours}$