Miguel is returning from a trip. In 4 hours, he has driven 2/3 of the total distance. He wants to know how long the total drive will take. At this rate, what is the total time it will take him to reach his destination?
If in 4 hours he has already traveled 2/3 of the total distance, then in 1 hour he has traveled 2/3รท4 = <<2/3/4=0.16666666666666666>>0.16666666666666666 of the distance
He travels 0.16666666666666666*1 = <<0.16666666666666666*1=0.16666666666666666>>0.16666666666666666 of the distance in one hour.
To travel the whole distance, he will use 1/0.16666666666666666 = <<1/0.16666666666666666=6.0>>6 hours. Answer: \boxed{6}.
To find out the total time it will take Miguel to reach his destination, we can use the information provided:
- In 4 hours, Miguel has driven 2/3 of the total distance.
Let's determine the time it will take him to drive the remaining 1/3 of the total distance.
If he has driven 2/3 of the distance in 4 hours, then the remaining 1/3 of the distance will take him the same amount of time.
We can set up a proportion to solve for x (the total time it will take him to reach his destination):
(2/3) / 4 = (1/3) / x
To solve this proportion, we can cross-multiply:
(2/3) * x = (1/3) * 4
Now, we can simplify and calculate x:
(2/3) * x = (1/3) * 4
2x/3 = 4/3
To isolate x, we can multiply both sides by the reciprocal of 2/3, which is 3/2:
(2x/3) * (3/2) = (4/3) * (3/2)
x = 12/6
x = 2
Therefore, the total time it will take Miguel to reach his destination is 2 hours.
To find the total time it will take Miguel to reach his destination, we need to determine how long it took him to drive 2/3 of the total distance. Then, we can calculate the remaining time needed to complete the trip.
Given that Miguel drove 2/3 of the total distance in 4 hours, we can set up the following equation:
(2/3) * Total distance = Distance driven
(2/3) * Total distance = 4
To isolate the total distance, we can multiply both sides of the equation by (3/2):
Total distance = (4 * 3/2)
Total distance = 6
Now that we know the total distance is 6, we can calculate how long the total drive will take for Miguel. Since he has already spent 4 hours driving 2/3 of the distance, the remaining 1/3 of the distance will take an additional t hours.
(1/3) * Total distance = Distance left
(1/3) * 6 = Distance left
2 = Distance left
To find the remaining time needed, we set up another equation:
(1/3) * Total drive time = Time needed for remaining distance
t = (1/3) * Total drive time
t = (1/3) * T
Now, we can substitute the value of the total distance (6) from the previous calculation:
t = (1/3) * 6
t = 2
Therefore, the total time it will take Miguel to reach his destination is 4 hours (for the first 2/3 of the distance) plus an additional 2 hours (for the remaining 1/3 of the distance). Therefore, Miguel's total drive time will be 6 hours.