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?
They separate at a rate of 44 + 48 = 92 mph. Divide 274 miles by 92 mph for the number of hours.
1.9 hours
To find out at what time the buses will be 274 miles apart, we need to divide the total distance between them by their combined rate of separation.
The first bus leaves at 1 P.M. and travels at an average rate of 44 miles per hour. The second bus leaves one hour later at 2 P.M. and travels at an average rate of 48 miles per hour.
The combined rate of separation of the two buses is the sum of their individual rates, which is 44 + 48 = 92 miles per hour.
To calculate the time it takes for them to be 274 miles apart, we divide the distance by the rate:
Time = Distance / Rate
Time = 274 miles / 92 miles per hour
Time ≈ 2.98 hours
Since time can be represented in hours and minutes, we need to convert 0.98 hours into minutes. Multiply 0.98 by 60 to get:
0.98 hours * 60 minutes/hour = 58.8 minutes ≈ 59 minutes (rounded to the nearest minute)
So, the buses will be approximately 274 miles apart after about 2 hours and 59 minutes.
To determine the final time when the buses will be 274 miles apart, we add this duration to the initial departure time of the first bus, which was 1 P.M.
Final Time = Initial Departure Time + Time Taken
Final Time ≈ 1 P.M. + 2 hours 59 minutes
Final Time ≈ 3 P.M. 59 minutes
Therefore, the buses will be approximately 274 miles apart at around 3 P.M. 59 minutes.