Problema Solution
A car travels along a straight stretch of road.
It proceeds for 13.7 mi at 53 mi/h, then
28.6 mi at 47 mi/h, and finally 43.2 mi at
36.6 mi/h.
What is the car’s average velocity during
the entire trip?
Answer in units of mi/h.
Answer provided by our tutors
Let
v = the average velocity
d = the total distance traveled
t = the total time of the travel
The formula for average velocity is:
v = d/t
Also we will use the formula:
t = d/v
For the first part of the trip: 13.7 mi at 53 mi/h we calculate the time (t1):
d1 = 13.7 mi
v1 = 53 mi/h
t1 = d1/v1
t1 = 17.3/53 h
For the second part of the trip: 28.6 mi at 47 mi/h we calculate the time (t2):
d2 = 28.6 mi
v2 = 47 mi/h
t2 = d2/v2
t2 = 28.6/47 h
For the third part of the trip: 43.2 mi at 36.6 mi/h we calculate the time (t3):
d3 = 43.2 mi
v3 = 36.6 mi/h
t3 = d3/v3
t3 = 43.2/36.6 h
The total distance traveled is:
d = d1 + d2 + d3
d = 13.7 + 28.6 + 43.2
d = 85.5 mi
The total time of the trip is:
t = t1 + t2 + t3
t = 17.3/53 + 28.6/47 + 43.2/36.6
t = 2.12 h
The average velocity during the entire trip is:
v = d/t
v = 85.5/2.12
v = 40.33 mph