On a rectangle of area A = HL traveled on a lane down the middle (along L) with the speed V 1 and along H with the speed V 0 , the area-averaged travel time is (See Fig. P XXXXXXXXXXThis time is...

On a rectangle of area A = HL traveled on a lane down the middle (along L) with the speed V₁
and along H with the speed V₀, the area-averaged travel time is

(See Fig. P13.25.) This time is minimal when H∕L = 2V₀∕V₁
and has the value

Assume next that A is shaped as a disc of radius R, where the travel is with only one speed (the lower speed, V₀). The travel is from all the

points of the disc to the center. The area is the same as before, 𝜋R²
= A. Find the expression for the area-averaged travel time t₀
from all the points of 𝜋R²
to the center. Determine the ratio between the average timest_0,1,_min
and t₀. How large must V₁∕V₀
be such that t_0,1,min
is shorter than t₀?