Word Problems: Cars Separating

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Two cars leave the same spot at the same time and travel in opposite directions.
If one car is traveling at 25 kph and
the other is traveling at 40 kph,
how long will it be until they are 520 km apart?

Draw a diagram of the start of this situation.

Draw a diagram of the final positions of the cars.

Define the variables for this problem.

The problem asks for a time, so the unknown is t, the time when the cars are 520 km apart.

Relate the 520 km to the distances traveled by each car.

Because the cars travel in opposite directions, the 520 is the sum of the distances traveled by each car.

How is each car's distance from the start related to the time, t?

For each car,
its distance = rate * time, or
its distance = (its speed) * t.

Write an equation summarizing this information.

520 = sum of the distances by each car, or
520 = (25 * t) + (40 * t)

Collect like terms.

520 = 65 * t

Divide by 65 on both sides.

, or t = 8

What should be the units on this result?

Since the rates are in km per hour, the time we calculate from the rates should be in hours.

Summarize these results.

After 8 hours, the cars are 520 km apart.

Check this result.

Using the speeds of the two cars, their distances from the starting point are 25 * 8 = 200, and 40 * 8 = 320 km.

Is this consistent with the original data about being 520 km. apart?

Yes. Since they travel in opposite directions, the total distance between the cars is the sum: 200 + 320 = 520 km.

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