GreenlightTestPrep wrote:
On a road trip, Kip drove one-quarter the distance at an average speed of v miles per hour, one-quarter the distance at an average speed of 2v miles per hour, one-quarter the distance at 4v miles per hour, and one-quarter the distance at 8v miles per hour. In terms of v, what was Kip’s average speed (in miles per hour) for the entire trip?
A) 15/4v
B) 15v/4
C) 32v/15
D) 4v/15
E) 15v/32
Since we aren't told the total distance, let's
assign a nice value to the distance.
Let's say
32 miles = TOTAL distance.
So, each quarter =
8 miles
Average speed = total distance/total travel timeSo, we must find the travel time for EACH QUARTER and add them together.
Time = distance/speed, so:
Time spent driving v mph =
8/v = 8/v
Time spent driving 2v mph =
8/2v = 4/v
Time spent driving 4v mph =
8/4v = 2/v
Time spent driving 8v mph =
8/8v = 1/v
TOTAL travel time = 8/v + 4/v + 2/v + 1/v
=
15/v Average speed = total distance/total travel time=
32/(
15/v)
= (
32)(
v/15)
= 32v/15
Answer: C
Cheers,
Brent