The family trip to Grandma's consisted of both a train ride and a car ride. The average speed of the train ride was
69 miles per hour, and the average speed of the car ride was
57 miles per hour. The entire trip lasted 9hours. Let x be the number of hours the train ride lasted. Write an expression for the total distance of the trip, in miles.
since distance = speed * time, that is
69x + 57(9-x)
To find the expression for the total distance of the trip, let's consider the time spent on each mode of transportation.
Let x be the number of hours the train ride lasted. Since the entire trip lasted 9 hours, the car ride lasted (9 - x) hours.
The distance traveled in the train ride can be calculated using the formula: Distance = Speed × Time. Therefore, the distance traveled by the train is 69x miles.
Similarly, the distance traveled in the car ride can be calculated as: Distance = Speed × Time. Therefore, the distance traveled by the car is 57(9 - x) miles.
To find the total distance of the trip, we need to add the distances traveled by the train and the car. Therefore, the expression for the total distance of the trip, in miles, is:
Total Distance = distance traveled by the train + distance traveled by the car
= 69x + 57(9 - x) miles
To find the expression for the total distance of the trip in miles, we need to understand that the distance traveled during the train ride is directly proportional to the time spent on the train. Let's first determine the distance traveled during each leg of the trip.
The speed of the train ride is given as 69 miles per hour, and the time spent on the train is represented by 'x' hours. Therefore, the distance traveled during the train ride is given by the expression 69x miles.
Similarly, the speed of the car ride is given as 57 miles per hour, and the time spent in the car is (9 - x) hours (since the entire trip lasted 9 hours and x hours were spent on the train). Hence, the distance traveled during the car ride is given by the expression 57(9 - x) miles.
To find the total distance of the trip, we add up the distances traveled during the train ride and the car ride. The expression for the total distance of the trip, in miles, is:
69x + 57(9 - x) = 69x + 513 - 57x = 12x + 513 miles.
Therefore, the expression for the total distance of the trip is 12x + 513 miles.