Melissa and Emily leave by car from the same location traveling in opposite directions. Melissa leaves at 4:00 traveling at 55mph. Emily leaves at 5:00 traveling at 60 mph. At what time will they be at 325 miles apart?
when they are 325 miles apart, Melissa went for t hrs
and Emily went for t-1 hours
55t + 60(t-1) = 325
55t + 60t - 60 = 325
115t = 385
t = 3.348 hrs or 3 hrs and 20.87 minutes
at 7:21 they will be 325 miles apart.
To find out at what time Melissa and Emily will be 325 miles apart, we can set up an equation based on their speeds and the time traveled.
Let's assume "t" represents the number of hours after Melissa leaves at 4:00.
Melissa's distance from the starting point can be expressed as: Distance = Speed * Time. In this case, Melissa's speed is 55 mph, and the extra hour she has traveled compared to Emily is (t + 1) hours. Therefore, Melissa's distance is: DistanceMelissa = 55 * (t + 1) miles.
Emily's distance from the starting point can be expressed as: Distance = Speed * Time. In this case, Emily's speed is 60 mph, and the time she has traveled is t hours (as she left an hour later). Therefore, Emily's distance is: DistanceEmily = 60 * t miles.
Since they are traveling in opposite directions, the total distance between them can be calculated by adding their individual distances: Total Distance = DistanceMelissa + DistanceEmily.
According to the problem, the total distance needs to be 325 miles. So, we have the equation:
325 = 55(t + 1) + 60t.
Now, we can solve this equation to find the value of t, which will tell us at what time Melissa and Emily will be 325 miles apart.
Let's simplify the equation:
325 = 55t + 55 + 60t.
Combine like terms:
325 = 115t + 55.
Move the constant term to the other side:
325 - 55 = 115t.
270 = 115t.
Divide both sides of the equation by 115:
t = 270 / 115.
t ≈ 2.35.
Therefore, Melissa and Emily will be 325 miles apart after approximately 2.35 hours.
To find at what time this will be, we need to take into account the time Melissa starts, which is 4:00. So, we add 2.35 hours to 4:00:
4:00 + 2 hours 21 minutes ≈ 6:21.
Therefore, Melissa and Emily will be 325 miles apart at approximately 6:21.