One car travels 200 miles in the same amount of time it takes a second car traveling 6 miles per hour slower than the first to go 176 miles. What are the speeds of the cars?The speed of the cars are miles per hour.
Question
One car travels 200 miles in the same amount of time it takes a second car traveling 6 miles per hour slower than the first to go 176 miles. What are the speeds of the cars?The speed of the cars are miles per hour.
Solution
Let's denote the speed of the first car as x (in miles per hour). Therefore, the speed of the second car is x - 6 mph.
The time it takes for each car to travel can be found using the formula time = distance / speed.
For the first car, the time is 200 miles / x mph.
For the second car, the time is 176 miles / (x - 6) mph.
Since the problem states that the times are equal, we can set the two times equal to each other and solve for x:
200 / x = 176 / (x - 6)
Cross-multiplying gives us:
200(x - 6) = 176x
Expanding and simplifying gives us:
200x - 1200 = 176x
Subtracting 176x from both sides gives us:
24x = 1200
Finally, dividing both sides by 24 gives us:
x = 50
So, the speed of the first car is 50 mph, and the speed of the second car is 50 - 6 = 44 mph.
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