HI,

There is a large number of commuters who decide to use either their  car or the tube. Commuting by train takes 70 minutes whatever the number of commuters taking the train. Commuting by car takes C(x) = 20 + 60x minutes, where x is the proportion of commuters taking their car, 0 <(or eual to)x<(or equal to)1. 

2. What is the proportion of commuters who will take their car if every-  one is taking her decision freely and independently so as to minimize her own commuting time? so to minimize their own commuting time the commutting time by car will equal 70. so 20+60x= 70 and x=0.83 so 83% of commuters will take their car Do you think this is right? Also,

3. What is the proportion of car users that minimizes the total commuting time? Am thinking the proportion of car users would be 0 as the minimum non-negative number and that would still be 20 minutes commuting by train.

Any help will be apprecited.

I didn't find the right solution from the Internet.

References:

https://www.thestudentroom.co.uk/showthread.php?t=2497704

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Thank you.