What is the distance between the two cities if my total traveling time was 32hrs?

Question

On a vacation I averaged 50 mph traveling from Denver to Minneapolis. Returning I took a different route that covered the same miles, and I averaged 55 mph. What is the distance between the two cities if my total traveling time was 32 hours

Answer 1

d=rt

d=50*t

d=55*(32-t)

50t=55*(32-t)

50t=1760-55t

50t+55t=1760

105t=1760

t=1760/105

t=16.7619 hours

d=50*16.7619

d=838.09 miles

 

another approach would be to find the average speed using the harmonic mean

mean=(2*50*55)/(50+55)

mean=5500/105

average rate=52.38095 mph

d=rt

d=52.38095*32

d=1676.19 miles which is the total distance

divide by 2

1676.19/2=838.09 miles again

 

 

 

Answer 2

Let x = one way distance

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Total time = 32

 

Therefore, x/50 + x/55 = 32

 

Multiply by the LCD, 550, to obtain 11x + 10x = 17600

 

                                                          21x = 17600

 

                                                             x ≈ 838 miles