Problem 221 - Prealgebra

Question

Road trip Noah was driving from Philadelphia to Cincinnati, a distance of 502 miles. He drove 115 miles, stopped for gas, and then drove another 230 miles before lunch. How many more miles did he have to travel?

Step-by-Step Solution

Answer

Noah has 157 miles left to travel.

Step 1 - Calculate Total Distance Traveled

First, add up the distances that were already traveled. Noah drove 115 miles first and then drove 230 miles.

Step 2 - Sum of distances traveled so far

Add the two segments of travel: 115 miles + 230 miles. This equals 345 miles.

Step 3 - Calculate Remaining Distance

Subtract the total distance traveled from the overall distance. The overall distance is 502 miles. The formula is: remaining distance = total distance - distance traveled so far. Therefore, remaining distance = 502 miles - 345 miles.

Step 4 - Solve the Equation

Perform the subtraction: 502 - 345 = 157 miles. Thus, Noah still has 157 miles to travel.

Key Concepts

distance calculation

Calculating the distance between two points is pivotal in many real-life scenarios, like planning a trip or determining how far you've traveled during a journey. In this exercise, the total distance from Philadelphia to Cincinnati is 502 miles.

To find the distance that has been traveled or is left to cover, you need to break it down into segments. Noah initially drove 115 miles and then another 230 miles, so the task is to find out how much more he must travel. Knowing how to segment and sum distances makes calculations manageable.

subtraction in word problems

Subtraction is a fundamental operation often used in solving word problems, like in this road trip scenario. When an exercise asks you to find 'how many more' or 'how much is left,' it typically means you'll need to subtract one quantity from another.

In Noah's road trip, we subtract the miles he has already driven from the total distance. This is a clear application of subtraction in word problems. With a total of 502 miles and 345 already traveled, we find the remaining distance by calculating 502 - 345. Easy steps like this make challenging problems more approachable.

step-by-step problem solving

Approaching problems step by step helps break down complex tasks into manageable parts, making it easier to find solutions. In our exercise, we broke it down into four steps:

1. Calculate Total Distance Traveled
2. Sum of Distances Traveled So Far
3. Calculate Remaining Distance
4. Solve the Equation

Starting by adding the miles Noah has already driven and then using subtraction to find the remainder simplifies the problem. This methodical approach ensures we don't overlook any details and reach the correct answer systematically.