A family left their house in two cars at the same time. One car traveled an average of 7 miles per hour faster than the order. When the first car arrived at the destination after 5 1/2 hours of driving, both cars had driven 599.5 miles. If the second car continues at the same average speed, how much time to the nearest minute before the second car arrives?
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If both cars had driven the same distance (599.5 miles) in the same time, they had the same average speed.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the speed of the first car is x miles per hour. The second car then travels at a speed of (x + 7) miles per hour.
First, we can find the distance traveled by the first car using the formula: distance = speed × time.
So, the distance traveled by the first car is 599.5 miles, and the time it takes is 5.5 hours.
Therefore, we have the equation: 599.5 = x × 5.5.
Next, we can find the time it takes for the second car to cover the same distance, 599.5 miles, at a speed of (x + 7) miles per hour.
To find this time, we can use the formula: time = distance ÷ speed.
So, the time taken by the second car is: 599.5 ÷ (x + 7).
To find the value of x, we can solve the first equation: 599.5 = x × 5.5.
Divide both sides of the equation by 5.5:
599.5 ÷ 5.5 = x.
Simplifying:
109 = x.
Now, we can substitute the value of x into the equation for the time taken by the second car:
time = 599.5 ÷ (x + 7) = 599.5 ÷ (109 + 7) = 599.5 ÷ 116 = 5.17 hours.
To find the time in minutes, we multiply the decimal part (0.17) by 60:
0.17 × 60 = 10.2 minutes.
Rounding the minutes to the nearest whole number, the second car will arrive in approximately 10 minutes.
Therefore, to the nearest minute, the second car will arrive in 5 hours and 10 minutes.