At 1:00 p.m., a car leaves a city and travels north at a rate of 55 mi/h. An hour later, a second car leaves the city and travels south at a rate of 60 mi/hr. At what time will the two cars be 285 miles apart
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To solve this problem, we need to determine the time it takes for the two cars to be 285 miles apart.
Let's break down the information we have:
1. The first car leaves the city at 1:00 p.m. and travels north at a rate of 55 mi/h.
2. The second car leaves the city one hour later, so it departs at 2:00 p.m., and it travels south at a rate of 60 mi/h.
To find the time at which the two cars are 285 miles apart, we can set up an equation based on the distance each car has traveled.
Let's assume that the time it takes for the two cars to be 285 miles apart is 't' hours.
For the first car:
Distance = Rate * Time
Distance = 55 * t
For the second car:
Distance = Rate * Time
Distance = 60 * (t - 1)
(Note: We subtract 1 hour from 't' since the second car departs one hour later.)
Since the cars are traveling in opposite directions, we can add up their distances to get the total distance between them:
55t + 60(t - 1) = 285
Now, let's solve this equation:
55t + 60t - 60 = 285
115t - 60 = 285
115t = 345
t = 345/115
t = 3
Therefore, it will take 3 hours for the two cars to be 285 miles apart.
To determine the time at which they will be 285 miles apart, we add the time it takes to the departure time of the second car:
2:00 p.m. + 3 hours = 5:00 p.m.
So, the two cars will be 285 miles apart at 5:00 p.m.