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Two airplanes left the same airport at the same time, flying in opposite directions. One flew at [tex]$400 \, \text{km/h}$[/tex] and the other flew at [tex]$250 \, \text{km/h}$[/tex]. In how many hours will the distance between the two planes be [tex]1625 \, \text{km}$[/tex]?



Answer :

GinnyAnswer
Certainly! Let's tackle this problem step-by-step:

1. Understanding the Problem:
- We have two airplanes leaving the same airport at the same time but flying in opposite directions.
- Airplane 1 flies at a speed of [tex]\( 400 \)[/tex] km/h.
- Airplane 2 flies at a speed of [tex]\( 250 \)[/tex] km/h.
- We need to find the time it takes for the distance between the two airplanes to be [tex]\( 1625 \)[/tex] km.

2. Concept of Relative Speed:
When two objects move in opposite directions, their relative speed is the sum of their speeds. This is because the distance between them increases at the rate of the sum of their individual speeds.

3. Calculating the Relative Speed:
- Speed of Airplane 1: [tex]\( 400 \)[/tex] km/h
- Speed of Airplane 2: [tex]\( 250 \)[/tex] km/h
- Relative Speed = Speed of Airplane 1 + Speed of Airplane 2
- Relative Speed = [tex]\( 400 \)[/tex] km/h + [tex]\( 250 \)[/tex] km/h = [tex]\( 650 \)[/tex] km/h

4. Using the Relative Speed to Find the Time:
We need to find the time taken for the distance between the two airplanes to reach [tex]\( 1625 \)[/tex] km. Time can be calculated using the formula:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \][/tex]

- Distance = [tex]\( 1625 \)[/tex] km
- Relative Speed = [tex]\( 650 \)[/tex] km/h

So,

[tex]\[ \text{Time} = \frac{1625 \text{ km}}{650 \text{ km/h}} \][/tex]

5. Performing the Division:
[tex]\[ \text{Time} = \frac{1625}{650} \text{ hours} \][/tex]

By simplifying:

[tex]\[ \text{Time} = 2.5 \text{ hours} \][/tex]

Therefore, the two airplanes will be [tex]\( 1625 \)[/tex] km apart after [tex]\( 2.5 \)[/tex] hours.

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