Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 miles per hour and the rest was along a highway, where his average speed was 60 miles per hour. The drive took 8 hours. What distance, in miles, did Minato drive along local roads?

The correct answer is: 45

We will solve each Option given and the value that satisfies all the conditions in the given question is our solution.
Step-by-step solution:-
Let the distance travelled, time taken and the speed at which Local roads were travelled be-
D1, T1 & S1 respectively.
Also, the distance travelled, time taken and the speed at which Highways were travelled be-
D2, T2 & S2 respectively.
For Option A,
D1 = 30, S = 20 Therefore, T1 = = = 1.5 hrs.
We know that the total time taken = 8 hrs & Time taken on Local Roads = T1 = 1.5 hrs.
Therefore, Time Taken on Highways = T2 = 8 - 1.5 = 6.5 hrs
We know that total distance travelled = 390 miles & Distance travelled on Local Roads = 30 miles
Therefore, Distance travelled on Highways = D2 = 390 - 30 = 360 miles
S2 = = = 55.38 which is not equal to the given value of S2 = 60
Therefore, Option A is eliminated.
For Option B,
D1 = 45, S = 20 Therefore, T1 = = = 2.25 hrs.
We know that the total time taken = 8 hrs & Time taken on Local Roads = T1 = 2.25 hrs.
Therefore, Time Taken on Highways = T2 = 8 - 2.25 = 5.75 hrs
We know that total distance travelled = 390 miles & Distance travelled on Local Roads = 45 miles
Therefore, Distance travelled on Highways = D2 = 390 - 45 = 345 miles
S2 = = = 60 which is equal to the given value of S2 = 60
Therefore, Option B is the correct answer.
Final Answer:-
Option B i.e. 45 is the correct Option.
Note:-
Alternatively, simultaneous equations can be formed using the conditions given in the question. However, due to multiple variables involved, calculation would get trickier. Hence, trial & error method is used in the solution.