a freight train is traveling 30mph. An automobile starts out from the same place 1 hour later and overtakes the train in 3 hours. What was the rate of the automobile?

in one hour the train moved 30 miles ahead.

The car made that up in 3 hours, so its speed was 10 mph greater than the train's.

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To find the rate of the automobile, we can use the formula distance = rate × time.

Let's first calculate the distance the freight train traveled in 4 hours since it started 1 hour earlier than the automobile:

Distance = Rate × Time
Distance = 30 mph × 4 hours
Distance = 120 miles

Since the automobile overtakes the train, the distance it travels is the same as the distance the train traveled, which is 120 miles.

Now, let's find the rate of the automobile using the formula:

Rate = Distance / Time
Rate = 120 miles / 3 hours
Rate = 40 mph

Therefore, the rate of the automobile is 40 mph.

To find the rate of the automobile, we can start by understanding the information given.

Let's assume that the rate of the automobile is represented by "a" mph.

We know that the freight train is traveling at a constant speed of 30 mph.

The automobile starts 1 hour later than the train, so by the time it starts, the train has already been traveling for 1 hour.

Now, let's analyze the scenario when the automobile overtakes the train. We are given that it takes 3 hours for the automobile to catch up to the train.

During these 3 hours, the train has been traveling for a total of 4 hours (1 hour before the automobile started + 3 hours after the automobile started).

Since both the automobile and the train have been traveling for the same amount of time when the automobile overtakes the train, we can set up the following equation:

Distance traveled by the train = Distance traveled by the automobile

Since distance = speed × time, we have:

30 mph × 4 hours = a mph × 3 hours

Simplifying the equation, we can isolate "a" to determine the rate of the automobile:

120 = 3a

Dividing both sides of the equation by 3, we find:

a = 40 mph

Therefore, the rate of the automobile is 40 mph.

In summary, to find the rate of the automobile, we set up an equation by equating the distances traveled by both the train and the automobile. By using the given information of time and speed, we solve for the rate of the automobile.