One car travels 105 miles in the same amount of time it takes a second car traveling 4 miles per hour slower than the first to go 93 miles. What are the speeds of the cars?The speed of the cars are miles per hour.
Question
One car travels 105 miles in the same amount of time it takes a second car traveling 4 miles per hour slower than the first to go 93 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 - 4 mph.
The time it takes for each car to travel their respective distances can be found using the formula time = distance/speed.
So, for the first car, the time is 105/x hours and for the second car, the time is 93/(x - 4) hours.
According to the problem, these times are equal. So we can set up the following equation:
105/x = 93/(x - 4)
To solve this equation, we can cross-multiply:
105*(x - 4) = 93*x
105x - 420 = 93x
Subtract 93x from both sides:
12x = 420
Divide by 12:
x = 35
So, the speed of the first car is 35 mph and the speed of the second car is 35 - 4 = 31 mph.
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