Earches related to 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. if the 288 dash mile trip took 6 hours, determine how long the bus traveled at each rate.

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

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

step-by-step explanation: