A bus leaves a station at 1 P.M., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the buses be 274 mi apart?
(44 mi/hr x time) + 44 mi = distance 1.
(48 mi/hr x time) = distance of 2.
Add them together.
(44 x time) + 44 + (48 x time) = d1 + d2.
d1 + d2 = 274 miles.
solve for time.
Post your work if you get stuck.
Let's start by breaking down the given information:
1. The first bus leaves the station at 1 P.M. and travels west at a rate of 44 mi/h.
2. The second bus leaves the station one hour later, so it leaves at 2 P.M., and travels east at a rate of 48 mi/h.
3. We need to find the time at which the buses will be 274 miles apart.
To solve this problem, we can use the formula for distance: distance = speed × time.
Let's assign variables to represent the time it takes for each bus to travel their respective distances:
Let t represent the time in hours for the first bus.
The distance traveled by the first bus is (44 mi/h) × t = 44t miles.
Since the second bus leaves one hour later than the first bus, the time for the second bus is t - 1.
The distance traveled by the second bus is (48 mi/h) × (t - 1) = 48(t - 1) miles.
According to the problem, the total distance between the buses is 274 miles, so we can write the equation:
44t + 48(t - 1) = 274
Now, we can solve this equation to find the value of t, which represents the time it takes for the buses to be 274 miles apart.
44t + 48t - 48 = 274
92t - 48 = 274
92t = 322
t = 322/92
t ≈ 3.5
Therefore, it will take approximately 3.5 hours for the buses to be 274 miles apart.
To find the time when the buses will be 274 miles apart, we need to add the time taken by the first bus to the starting time of 1 P.M.
1 P.M. + 3.5 hours = 4:30 P.M.
So, the buses will be 274 miles apart at 4:30 P.M.