A Freight train is traveling 30 miles per hour. 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?
the train went for 4 hours at 30 mph, so it went 120 miles
the car also went 120 miles but only took 3 hours , let its rate be x mph
so solve:
3x = 120
Let's calculate the distance covered by the freight train before the automobile overtakes it. Assuming the freight train travels at a constant speed of 30 miles per hour:
Distance covered by the freight train = Speed × Time
Distance covered by the freight train = 30 miles/hour × (1 hour + 3 hours)
Since the freight train travels for a total of 4 hours, the distance it covers is:
Distance covered by the freight train = 30 miles/hour × 4 hours
Distance covered by the freight train = 120 miles
Now, let's find the rate of the automobile. We know that it overtakes the freight train in 3 hours:
Rate of the automobile = Distance covered by the automobile / Time taken by the automobile
Rate of the automobile = 120 miles / 3 hours
Rate of the automobile = 40 miles per hour
Therefore, the rate of the automobile is 40 miles per hour.
To find the rate of the automobile, we can use the concept of relative speed.
Let's assume the rate of the automobile is "A" miles per hour.
Since the automobile starts 1 hour after the train, the train would have covered a distance of 30 miles in that 1 hour (since the train travels at a rate of 30 miles per hour).
Now, let's consider the time it takes for the automobile to overtake the train. We are given that the automobile overtakes the train in 3 hours. During this time, the train would have been traveling for 1 hour more than the automobile. So, the total time the train has been traveling is (3 + 1) = 4 hours.
Now, let's calculate the distance covered by the train during the time the automobile was traveling: Distance = Rate x Time
Distance covered by the train = 30 miles per hour x 4 hours = 120 miles
Since the automobile overtakes the train, it covers the same distance as the train. Hence, the rate of the automobile (A) can be calculated as follows:
Distance covered by the automobile = Rate x Time
120 miles = A miles per hour x 3 hours
Simplifying the equation:
120 miles = 3A miles per hour
Dividing both sides of the equation by 3:
40 miles = A miles per hour
Therefore, the rate of the automobile is 40 miles per hour.