The average speed of one airplane is 200 mph faster than that of an automobile. if the automobile starts at 3 a. m. and the airplane starts from the same place at 11 a. m., they will have traveled the same number of miles by 1: 00 p. m. if r represents the rate of the automobile, how many miles does the plane travel? 200r 2(200 + r) 10r

Distance = 500 miles

Step-by-step explanation:

Step 1: Write the data of speed, distance and time for aeroplane and automobile.

Automobile:

Speed = r

Time = 10 hours (3 am till 1 pm)

Distance = SxT

Distance = r x 10 = 10r

Aeroplane:

Speed = 200 + r (200 mph more than automobile)

Time = 2 hours ( 11 am till 1 pm)

Distance = SxT

Distance = 2x(200+r) = 400+2r

Step 2: Equate both distances to find the value of r

Distance of automobile = Distance of aeroplane

10r = 400 + 2r

8r = 400

r = 50

Step 3: Find the distance using any one equation

Distance of automobile = 10r

r = 50

Distance = 10 x 50 = 500 miles

Therefore, the plane travels 500 miles.

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step-by-step explanation: