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Michael drove from home to work at an average speed of 50 mph. His return trip home took 30 minutes longer because he could only drive at 40 mph. Find the distance from his home to his work. A. [3 pts) Define variables to represent the unknowns and setup the necessary equations to answer the question. B. [4 pts) Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units. (You will not receive full credit if a trial and error method is used in place of an algebraic method.)

Respuesta :

fichoh

Answer:

100 miles

Step-by-step explanation:

Given :

To work :

speed = 50mph

Let time taken = x

From work :

speed = 40mph

30 minutes = 30/60 = 0.5

Time taken = x + 0.5

Distance from home to work :

Distance = speed * time

To work distance = from work distance

This can be algebraically expressed as :

50 * x = 40(x + 0.5)

50x = 40x + 20

50x - 40x = 20

10x = 20

x = 20/10

x = 2

Hence,

Distance = 50 * 2 = 100

The the distance from home to work = 100 miles

raphealnwobi

The distance from Michael home to work is 100 miles

Speed

Speed is the ratio of the total distance travelled to the total time taken. It is given by:

Speed = distance / time

Let d represent the distance from Michael home to work. Hence:

  • 50 = d/t
  • t = d / 50

He took 30 minutes (0.5 hours) longer when driving at 40 mph, hence:

  • 40 = d/(t + 0.5)
  • t = (d - 20)/40

d/50 = (d - 20) / 40

40d = 50d - 1000

10d = 1000

d = 100 miles

The distance from Michael home to work is 100 miles

Find out more on speed at: https://brainly.com/question/4931057

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