What was the cars average speed over the entire travel time?

Question

a car travels for 55 minutes at a speed of 65 mph, and 45 minutes at a speed of 35 mph.

Answer 1

distance=rate*time

d=65*(55/60)

d=65*(11/12)

d=715/12

d=59.58333... miles driven

 

d=35*(45/60)

d=35*(3/4)

d=105/4

d=26.25 miles driven

 

total distance=rate*(total time)

59.58333...+26.25=85.8333... miles driven altogether

(11/12)+(3/4)=(11/12)+(9/12)=20/12=5/3 hours total time

note: 0.8333...=5/6, so total distance=85 5/6 miles

85 5/6=rate*(5/3)

515/6=rate*(5/3)

multiply both sides by 3/5

(3/5)(515/6)=rate*(5/3)(3/5)

simplifying the left side...

103/2=rate

51.5=rate

average speed (rate) is 51.5 miles per hour

notice that the average speed is closer to 65 mph than to 35 mph because you spend more time (55 min) at 65 mph than at 35 mph (only 45 min)

Answer 2

Method One:

(45 thirty-fives plus 55 sixty-fives) divided by a total of (45 + 55) = 

 

45 x 35 +  55 x 65

---------------------   =   51.5 which seems reasonable

       45 + 55

 

Method Two.

 

55/60 hr   x   65mi/hr  =  59.58333333.... mi

 

45/60 hr   x   35mi/hr  =  26.25000000.... mi

 

Total distance              = 85.83333333..... mi

 

Time for the 85.333... miles is (45+55) min = 100 min. = 100/60 hr = 1.6666.... hr

 

Avg.Speed = 85.8333.... mi /  1.6666... hr  = 51.5 miles per hour