Problema Solution
Suppose you are entered in a driving contest - and you are expected to maintain an average speed of 60 MPH for two miles. Unfortunately, your engine develops a miss and you can only average 30 MPH for the first mile. How fast must you drive the second mile in order to meet the average speed requirement?
Answer provided by our tutors
let
v1 = 30 mph the average speed for the first mile
v2 = the average speed for the second mile
since speed = distance/time we have time = distance/speed
60 = 2/(1/v1 + 1/v2)
(1/v1 + 1/v2) = 2/60
(1/30 + 1/v2) = 1/30
1/v2 = 0
we conclude that the driver will never average 60 mph not matter how big is the average speed for the second mile.
Another way to conclude this is:
the time of the driving 60 mph for 2 miles is:
2/60 = 1/30 hr
the time for driving 30 mph for 1 mile is also:
1/30 hr
thus no mater how fast the driver drives for the second mile he will always pass the 2 miles distance in a longer time period of 1/30 hours thus he will never meet the average speed requirements.