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?
Use the same method indicated in my response to your previous post.
Thanks for asking.
To solve this problem, let's use the formula:
Time = Distance / Rate
Let's denote the driving time on the first day as T1, and the driving time on the second day as T2. We are given that Ariana took 2 hours longer to drive 360 miles on the first day than she took to drive 270 miles on the second day.
We can set up two equations based on the formula:
T1 = 360 / R (Equation 1)
T2 = 270 / R (Equation 2)
where R represents the speed (rate) at which Ariana was driving both days.
Since we are given that the speed was the same on both days, we can equate T1 and T2 and solve for the driving time on each day.
360 / R = 270 / R + 2
To solve for T1, we need to isolate T1 on one side of the equation. Here's how:
1. Multiply both sides of the equation by R to eliminate the denominator:
360 = 270 + 2R
2. Subtract 270 from both sides:
90 = 2R
3. Divide both sides by 2 to solve for R:
R = 45
Now that we have the rate, we can substitute it back into Equation 1 to solve for T1:
T1 = 360 / 45
T1 = 8 hours
Therefore, Ariana took 8 hours to drive on the first day and 270 / 45 = 6 hours to drive on the second day.