Ariana took 2 h longer to drive 360 mi on the first day of
a trip than she took to drive 270 mi on the second day. If her speed was the same
on both days, what was the driving time each day?
Start with time, t. If t is the time in hours the first day, then t-2 is the time for the second day.
speed=distance/time
first day: speed=360/t
Second day: speed=270/(t-2)
the speeds both day were the same, so set them equal and solve for t.
Start with time, t. If t is the time in hours the first day, then t-2 is the time for the second day.
speed=distance/time
first day: speed=360/t
Second day: speed=270/(t-2)
the speeds both day were the same, so set them equal and solve for t.
To find the driving time for each day, you can start by setting up a system of equations based on the given information.
Let's set the time for the first day as t hours. Since Ariana took 2 hours longer on the first day, the time for the second day would be (t - 2) hours.
Using the formula: speed = distance/time, we can determine the speeds for each day.
For the first day: speed = 360 miles / t hours
For the second day: speed = 270 miles / (t - 2) hours
Since the speeds for both days were the same, we can set the two speeds equal to each other and solve the equation for t.
360/t = 270/(t - 2)
To simplify the equation, we can cross-multiply:
360(t - 2) = 270t
Expanding and rearranging the equation:
360t - 720 = 270t
Subtracting 270t from both sides:
90t - 720 = 0
Adding 720 to both sides:
90t = 720
Dividing both sides by 90:
t = 8
So, the time for the first day was 8 hours. Since the time for the second day was 2 hours less, the time for the second day would be:
t - 2 = 8 - 2 = 6 hours
Therefore, Ariana drove for 8 hours on the first day and 6 hours on the second day.