a busleaves a station at 1 pm, 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 two buses be 274 mi apart?
The distance traveled apart in the first hour si 44mi/hr * 1 hr.
The additional distance traveled after that hour is
44*t + 48*t
so, the total distance apart at time t is 44*1 + 44*t + 48*t
set that equal to 274mi, and solve for t.
To find the time when the two buses will be 274 miles apart, let's create an equation.
Let's assume that t represents the number of hours after the second bus leaves the station.
In the first hour, the distance traveled apart is 44 miles since the first bus has been traveling west at a rate of 44 miles per hour.
After the first hour, the distance traveled apart will be the sum of the distances covered by both buses. The first bus travels at a rate of 44 miles per hour, and the second bus travels at a rate of 48 miles per hour. So, the equation representing the additional distance traveled after the first hour is:
44t + 48t
Now, let's add the distance covered in the first hour (44 miles) to the additional distance traveled after the first hour (44t + 48t) to get the total distance apart at time t:
44 * 1 + 44t + 48t = 274
Simplifying the equation:
44 + 44t + 48t = 274
Combining like terms:
92t + 44 = 274
Subtracting 44 from both sides:
92t = 230
Dividing both sides by 92:
t = 2.5
Therefore, the two buses will be 274 miles apart after 2.5 hours.
To find the exact time, we need to add this time (2.5 hours) to the time the first bus left the station. The first bus left at 1 pm, so adding 2.5 hours to 1 pm:
1 pm + 2.5 hours = 3:30 pm
So, the two buses will be 274 miles apart at 3:30 pm.