Question

In the following exercise, translate to an equation or inequality and solve.

Two planes leave Dallas at the same time. One heads east at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per hour. How many hours will it take them to be 2,025

miles apart?

Short answer

The required time is$2.5hr$

Step-by-step solution

Step 1. Given Information

We are given that two planes leave at the same time. One plane heads east at the speed of 428mph, second plane heads west at the speed of 382mph.

Step 2. Translation 

We will create the table to organise the information and let $t$is the required time.

	$Dis\tan ce=Rate\times time$	Time
East	428 mph	$t$	$428t$
West	382 mph	$t$	$382t$
2025 miles

As total distance given is 2025 miles. Thus, the required equation is$428t+382t=2025$

Step 3. Calculation 

Solve the equation to find the value.

$$\begin{gathered} 428t+382t=2025 \\ 810t=2025 \\ t=2.5hr \end{gathered}$$

Hence, the required time is$2.5hr$