Math / Algebra

QuestionEquations and urequanue Writing a multi-step equation for a realworld situation Español
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 53 miles per hour. The entire trip lasted 7 hours.
Let $x$ be the number of hours the train ride lasted. Write an expression for the total distance of the trip, in miles. total distance (in miles) $=$ $\square$ $\square$ $\square$

Studdy Solution

STEP 1

1. The train ride and car ride together lasted a total of 7 hours.
2. The average speed of the train ride was 69 miles per hour.
3. The average speed of the car ride was 53 miles per hour.
4. $x$ represents the number of hours the train ride lasted.

STEP 2

1. Express the time for the car ride in terms of $x$ .
2. Write an expression for the distance traveled by train.
3. Write an expression for the distance traveled by car.
4. Combine the expressions to find the total distance.

STEP 3

Since the entire trip lasted 7 hours and $x$ is the time for the train ride, the time for the car ride is $7 - x$ hours.

STEP 4

The distance traveled by train is the product of the train's speed and the time spent on the train. Thus, the distance by train is $69x$ miles.

STEP 5

The distance traveled by car is the product of the car's speed and the time spent in the car. Thus, the distance by car is $53(7 - x)$ miles.

STEP 6

The total distance of the trip is the sum of the distances traveled by train and car. Therefore, the total distance is:
$69x + 53(7 - x)$
The expression for the total distance of the trip, in miles, is:
$\boxed{69x + 53(7 - x)}$

Was this helpful?

Studdy Solution

STEP 1

1. The train ride and car ride together lasted a total of 7 hours.
2. The average speed of the train ride was 69 miles per hour.
3. The average speed of the car ride was 53 miles per hour.
4. $x$ represents the number of hours the train ride lasted.

STEP 2

1. Express the time for the car ride in terms of $x$ .
2. Write an expression for the distance traveled by train.
3. Write an expression for the distance traveled by car.
4. Combine the expressions to find the total distance.

STEP 3

Since the entire trip lasted 7 hours and $x$ is the time for the train ride, the time for the car ride is $7 - x$ hours.

STEP 4

The distance traveled by train is the product of the train's speed and the time spent on the train. Thus, the distance by train is $69x$ miles.

STEP 5

The distance traveled by car is the product of the car's speed and the time spent in the car. Thus, the distance by car is $53(7 - x)$ miles.

STEP 6

The total distance of the trip is the sum of the distances traveled by train and car. Therefore, the total distance is:
$69x + 53(7 - x)$
The expression for the total distance of the trip, in miles, is:
$\boxed{69x + 53(7 - x)}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The train ride and car ride together lasted a total of 7 hours.2. The average speed of the train ride was 69 miles per hour.3. The average speed of the car ride was 53 miles per hour.4. x x x represents the number of hours the train ride lasted.

STEP 2

1. Express the time for the car ride in terms of x x x.2. Write an expression for the distance traveled by train.3. Write an expression for the distance traveled by car.4. Combine the expressions to find the total distance.

STEP 3

Since the entire trip lasted 7 hours and x x x is the time for the train ride, the time for the car ride is 7−x 7 - x 7−x hours.

STEP 4

The distance traveled by train is the product of the train's speed and the time spent on the train. Thus, the distance by train is 69x 69x 69x miles.

STEP 5

The distance traveled by car is the product of the car's speed and the time spent in the car. Thus, the distance by car is 53(7−x) 53(7 - x) 53(7−x) miles.

STEP 6

The total distance of the trip is the sum of the distances traveled by train and car. Therefore, the total distance is:69x+53(7−x) 69x + 53(7 - x) 69x+53(7−x) The expression for the total distance of the trip, in miles, is:69x+53(7−x) \boxed{69x + 53(7 - x)} 69x+53(7−x)​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The train ride and car ride together lasted a total of 7 hours.
2. The average speed of the train ride was 69 miles per hour.
3. The average speed of the car ride was 53 miles per hour.
4. $x$ represents the number of hours the train ride lasted.

1. Express the time for the car ride in terms of $x$ .
2. Write an expression for the distance traveled by train.
3. Write an expression for the distance traveled by car.
4. Combine the expressions to find the total distance.

Since the entire trip lasted 7 hours and $x$ is the time for the train ride, the time for the car ride is $7 - x$ hours.

The distance traveled by train is the product of the train's speed and the time spent on the train. Thus, the distance by train is $69x$ miles.

The distance traveled by car is the product of the car's speed and the time spent in the car. Thus, the distance by car is $53(7 - x)$ miles.

The total distance of the trip is the sum of the distances traveled by train and car. Therefore, the total distance is:
$69x + 53(7 - x)$
The expression for the total distance of the trip, in miles, is:
$\boxed{69x + 53(7 - x)}$