Two cars are 30 miles apart and moving toward each other on the same highway. One car is going 10 miles per hour faster than the other. How fast is each of the cars going if they pass each other 15 minutes later?
speed of slower car --- x mph
speed of faster car ---- x+10
after 1 5minutes or 1/4 hour,
(1/4)x + (1/4)(x+10) = 30
x + x+10 = 300
carry on
To solve this problem, we can break it down into two steps. First, we need to calculate the relative speed at which the cars are approaching each other, and then we can use this information to determine the speed of each car.
Step 1: Calculate the relative speed of the two cars:
Since the cars are moving towards each other, we can consider their speeds as additive. Let's call the speed of the slower car "x" miles per hour. Then, the speed of the faster car will be "x + 10" miles per hour.
Given that the time taken to pass each other is 15 minutes, we need to convert this time into hours. Since 1 hour = 60 minutes, 15 minutes is equal to 15/60 = 1/4 hour.
The relative speed is the sum of the speeds of the two cars:
Relative Speed = Speed of Car 1 + Speed of Car 2
Relative Speed = x + (x + 10)
Step 2: Determine the speed of each car:
Now, we know that the relative speed is equal to the distance traveled divided by the time taken. In this case, the distance between the cars is 30 miles, and they pass each other in 1/4 hour.
Relative Speed = Distance/Time
x + (x + 10) = 30/(1/4)
To simplify the equation, let's convert the right side to hours:
30/(1/4) = 30 * 4/1 = 120 mph
Now, we can solve for "x" by rearranging the equation:
2x + 10 = 120
2x = 120 - 10
2x = 110
x = 55
Therefore, the speed of the slower car is 55 mph, and the speed of the faster car is 55 + 10 = 65 mph.