time for first trip = d/x
time for return = d/y
total time = (d/x + d/y)
= (dy + dx)/(xy) = d(x+y)/(xy)
total distance = 2d
average speed = 2d/( d(x+y)/(xy) )
= 2xy/(x+y) = 50
xy/(x+y) = 25
xy = 25x + 25y
25y - xy = 25x
y(25 - x) = -25x
y = 25x/(x-25)
e.g. let x = 50, then y = 50
let x = 30, then y = 150
let x = 26, then y = 650
let x = 24.9, then y = 6225
as x ---> 25, y becomes infinitely large
Consider a trip of 600 km, x = 30 with y = 150
time at slower speed = 600/30 = 20 hrs
time of return at 150 = 600/150 = 4 hrs
total time = 24 hrs, total distance = 1200
avg speed = 1200/24 = 50 , OK
Now the same trip at a first speed of 26 mph
time for first trip = 600/26 = 23.076 hrs, so all the time needed to make a trip of 1200 miles at 50 mph has just about been used up, and the return trip would have to be at 650 mph.
At just about 25 mph, we would have used all the 24 hrs needed to get an average of 50 mph for a 1200 mile trip.
On a trip of d miles to another city, a truck driver's average speed was x miles per hour. On the return trip the average speed was y miles per hour. The average speed for the round trip was 50 miles per hour.
Show that y=25x/(x-25)
Find the limit of y as x approaches 25 from the right and interpret its meaning.
1 answer
1 answer