Two cars leave town at the same time and travel in opposite directions. The average speed of one car is 15 mph faster than the average rate of speed of the other car. The Carrs are 375 miles apart after 3 hours. Find the average speed rate of the two cars.
Guys please help me with this! I've tried 3 times, first was mph >100 which isn't reasonable, and the other times I kept on eliminating the variable all together (like 0 = 330) which I know is incorrect. I think the correct equations are x = y+15 and 3x - 3y = 375 but I'm really confused on this one. Please show me how to solve it .-.
speed of slower car --- x
speed of faster car ---- x + 15
3x + 3(x+15) = 375
6x + 45 = 375
6x = 330
x = 55
so speeds are 55 and 70 mph
check:
slower car went 3(55) or 165 miles
faster care went 3(70) or 210 miles
165 + 210 = 375
Thank you Reiny!!
Let's assume that the average speed of the first car is x mph.
The average speed of the second car will be (x + 15) mph since it is 15 mph faster than the first car.
The formula for distance is speed multiplied by time:
Distance = Speed * Time
After 3 hours, the first car will have traveled a distance of 3x miles, and the second car will have traveled a distance of 3(x + 15) miles.
Since they are traveling in opposite directions, the total distance between them is the sum of the distances traveled by both cars: 3x + 3(x + 15)
According to the problem, the total distance between them is 375 miles:
3x + 3(x + 15) = 375
Now, let's solve for x:
3x + 3x + 45 = 375
6x + 45 = 375
6x = 375 - 45
6x = 330
x = 330/6
x = 55
Therefore, the average speed of the first car is 55 mph, and the average speed of the second car is 55 + 15 = 70 mph.
To solve this problem, let's assign variables to represent the average speeds of the two cars. Let's say that the average speed of one car is x mph, and since the other car is traveling 15 mph faster, the average speed of the other car is (x + 15) mph.
The distance covered by each car in 3 hours can be calculated using the formula: distance = speed × time. For the first car, the distance traveled is 3x miles, and for the second car, the distance traveled is 3(x + 15) miles.
Since the two cars are traveling in opposite directions, the sum of the distances traveled by both cars will equal the total distance between them, which is 375 miles. Therefore, we can set up the following equation:
3x + 3(x + 15) = 375
Now let's solve the equation step by step:
3x + 3x + 45 = 375
6x + 45 = 375
6x = 375 - 45
6x = 330
x = 330 / 6
x = 55
So, the average speed of one car is 55 mph. Since the other car is traveling 15 mph faster, its average speed is (55 + 15) mph, which is 70 mph.
Therefore, the average speed of the two cars is 55 mph and 70 mph.