Final answer:
By using the concept of relative speed, we established the speed of the slower car as 65 mph and the faster car as 75 mph after they were 420 miles apart in three hours.
Step-by-step explanation:
To solve the problem of two cars traveling in opposite directions with one car traveling 10 miles per hour faster than the other and determining their speeds after they are 420 miles apart in three hours, we use the concept of relative speed. Let's denote the speed of the slower car as x miles per hour (mph). Then the speed of the faster car is (x + 10) mph. Since they are moving in opposite directions, their speeds add up when calculating the distance between them.
The total distance covered by both cars in 3 hours is:
Total distance = Speed of Car 1 × Time + Speed of Car 2 × Time
= x × 3 + (x + 10) × 3
= 3x + 3x + 30
= 6x + 30
We know from the problem statement that after 3 hours they are 420 miles apart, so we can write: 420 = 6x + 30
Now, solving for x: 390 = 6x x = 65 mph
Thus, the speed of the slower car (Car 1) is 65 mph and the speed of the faster car (Car 2) is 75 mph. The correct answer is (b) Car 1: 65 mph, Car 2: 75 mph.