Car 1 departs from City A at 8:00 AM and travels along a straight highway toward City B at a constant speed of miles per hour. At 8:30 AM, Car 2 departs from City B and travels along the same highway toward City A at a constant speed of miles per hour. At 9:15 AM, Car 1 encounters heavy traffic and reduces its speed by percent, maintaining this reduced speed for the rest of its journey, while Car 2 continues at its original speed. If the two cars pass each other at exactly 10:00 AM, what is the distance, in miles, between City A and City B?
Answer: 182.5 miles
Answer
The distance between City A and City B is 182.5 miles.
The total distance between the two cities is the sum of the distances traveled by both cars prior to their meeting point at 10:00 AM. Car 1 travels for 1.25 hours at 50 mph (62.5 miles) and 0.75 hours at 40 mph (30 miles), totaling 92.5 miles. Car 2 travels for 1.5 hours at 60 mph (90 miles). Summing these gives 92.5 + 90 = 182.5 miles.
Step-by-Step Solution
Key Concept
Converging motion with variable rates and time offsets