One car travels 105 miles in the same amount of time it takes a second car traveling 6 miles per hour slower than the first to go 87 miles. What are the speeds of the cars?
since time=distance/speed,
105/s = 87/(s-6)
s = 35 mi/hr
To determine the speeds of the cars, we can set up a system of equations. Let's call the speed of the first car "x" and the speed of the second car "x - 6" (since it is traveling 6 miles per hour slower).
The distance covered by each car can be determined using the formula: Distance = Speed × Time.
From the given information, we can set up the following equations:
For the first car: 105 = x × Time1
For the second car: 87 = (x - 6) × Time2
Since the question states that both cars take the same amount of time to travel their respective distances, we can equate the times:
Time1 = Time2
Now, we can rearrange the equations to isolate the unknowns:
Time1 = 105 / x
Time2 = 87 / (x - 6)
Since the times are equal, we can set up the equation:
105 / x = 87 / (x - 6)
To solve this equation, we can cross-multiply:
105(x - 6) = 87x
Expanding the equation:
105x - 630 = 87x
Combining like terms:
105x - 87x = 630
18x = 630
Dividing both sides by 18:
x = 35
Therefore, the speed of the first car is 35 mph.
To find the speed of the second car, we can substitute the value of x back into the equation:
x - 6 = 35 - 6 = 29
Hence, the speed of the second car is 29 mph.