Question

If Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1/2 of the trip to drive. What was the total length, in miles, of his trip?

• A. 360
• B. 180
• C. 120
• D. 60
• E. 90

Hint:

An alternative way to set up the equation is to consider the fraction of the trip covered. Dave drove 1/3 and had 1/2 left. The fraction of the trip he drove on the second day must be the difference: \( 1 - \frac{1}{3} - \frac{1}{2} = \frac{6-2-3}{6} = \frac{1}{6} \). So, 60 miles represents 1/6 of the total trip. If \( \frac{1}{6}D = 60 \), then \( D = 360 \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a word problem that can be solved by setting up an algebraic equation based on the fractions of the total distance. The total distance is the sum of the parts driven and the part remaining.

Step 2: Detailed Explanation:
Let \( D \) be the total length of the trip in miles.
On the first day, Dave drove one-third of the distance.
Distance driven on Day 1 = \( \frac{1}{3}D \).
On the second day, he drove 60 miles.
Distance driven on Day 2 = 60.
The total distance driven so far is the sum of the distances from Day 1 and Day 2.
Total distance driven = \( \frac{1}{3}D + 60 \).
The remaining distance is one-half of the total trip.
Remaining distance = \( \frac{1}{2}D \).
The sum of the distance driven and the distance remaining must equal the total distance of the trip.
\[ (\text{Distance driven}) + (\text{Remaining distance}) = \text{Total distance} \] \[ \left(\frac{1}{3}D + 60\right) + \frac{1}{2}D = D \] Now, we solve this equation for \( D \).
Combine the terms with \( D \):
\[ \frac{1}{3}D + \frac{1}{2}D + 60 = D \] To add the fractions, find a common denominator, which is 6.
\[ \frac{2}{6}D + \frac{3}{6}D + 60 = D \] \[ \frac{5}{6}D + 60 = D \] Subtract \( \frac{5}{6}D \) from both sides to isolate the constant term.
\[ 60 = D - \frac{5}{6}D \] \[ 60 = \frac{6}{6}D - \frac{5}{6}D \] \[ 60 = \frac{1}{6}D \] Multiply both sides by 6 to find \( D \).
\[ D = 60 \times 6 = 360 \]

Step 3: Final Answer:
The total length of the trip was 360 miles.