246 views

0 votes

Four cars need to travel from Akala $\text{(A)}$ to Bakala $\text{(B)}$. Two routes are available, one via Mamur $\text{(M)}$ and the other via Nanur $\text{(N)}$. The roads from $\text{A}$ to $\text{M}$, and from $\text{N}$ to $\text{B}$, are both short and narrow. In each case, one car takes $6$ minutes to cover the distance, and each additional car increases the travel time per car by $3$ minutes because of congestion. (For example, if only two cars drive from $\text{A}$ to $\text{M}$, each car takes $9$ minutes.) On the road from $\text{A}$ to $\text{N}$, one car takes $20$ minutes, and each additional car increases the travel time per car by $1$ minute. On the road from $\text{M}$ to $\text{B}$, one car takes $20$ minutes, and each additional car increases the travel time per car by $0.9$ minute.

The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.

A new one-way road is built from $\text{M}$ to $\text{N}$. Each car now has three possible routes to travel from $\text{A}$ to $\text{B}$: $\text{A-M-B, A-N-B}$ and $\text{A-M-N-B}$. On the road from $\text{M}$ to $\text{N}$, one car takes $7$ minutes and each additional car increases the travel time per car by $1$ minute. Assume that any car taking the $\text{A- M-N-B}$ route travels the $\text{A-M}$ portion at the same time as other cars taking the $\text{A-M-B}$ route, and the $\text{N-B}$ portion at the same time as other cars taking the $\text{A-N-B}$ route.

If all the cars follow the police order, what is the minimum travel time (in minutes) from $\text{A}$ to $\text{B}?$ (Assume that the police department would never order all the cars to take the same route.)

- $26$
- $32$
- $29.9$
- $3$