Answer: the bus traveled 144 miles at a speed of 60 miles per hour and 144 miles at a speed of 40 miles per hour
Step-by-step explanation:
The bus traveled at an average rate of 60 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip.
Let x miles = distance travelled at 60 miles per hour.
Let y miles = distance travelled at 40 miles per hour.
Total distance travelled = 288 miles.
Therefore,
x + y = 288 - - - - - - - 1
Total time spent in travelling 288 miles = 6 hours
Speed = distance /time
Time = distance / speed
Time spent when travelling x miles at a speed of 60 miles per hour = x/60
Time spent when travelling y miles at a speed of 40 miles per hour = y/40
Since total time is 6 hours, this means that
x/60 + y/40 = 6
(2x + 3y)/120 = 6
2x + 3y = 6 × 120 = 720 - - - - - - - 2
Substituting x = 288-y from equation 1 into equation 2, it becomes
2(288-y) + 3y= 720
576 - 2y + 3y = 720
- 2y + 3y = 720 - 576
y = 144 miles
x = 288 - y = 288-144
x = 144 miles
