Miguel is returning from a trip. In four 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
A: 8 hours
B: 12 hours
C: 8 hours
D: 8/3 hours
To calculate the total time it will take Miguel to reach his destination, we need to find the remaining distance and add it to the time he has already spent driving.
Given that Miguel has driven 2/3 of the total distance in 4 hours, we can determine that the remaining distance is 1/3 of the total distance.
Now, since it took Miguel 4 hours to drive 2/3 of the distance, the remaining 1/3 will also take the same amount of time.
To find the time it will take Miguel to drive the remaining 1/3 of the distance, we can use the concept of ratios. The ratio of the remaining distance to the time Miguel has already spent driving is 1:2/3.
Let's set up a proportion to find the time it will take Miguel to drive the remaining distance:
1/3 / x = 2/3 / 4
Cross-multiply the proportions:
1/3 * 4 = 2/3 * x
4/3 = 2x/3
Multiply both sides by 3 to get rid of the denominator:
4 = 2x
Divide both sides by 2:
x = 2
Therefore, it will take Miguel an additional 2 hours to drive the remaining 1/3 of the distance.
Adding this additional time to the 4 hours he has already spent driving, the total time it will take Miguel to reach his destination is:
4 hours + 2 hours = 6 hours
Therefore, the correct answer is not listed among the options provided.
If Miguel has driven 2/3 of the total distance in 4 hours, then he covered 1/3 of the distance in 4 hours. This means that it will take him 12 hours to cover the remaining 2/3 of the total distance (since 4 hours is equal to 1/3 of the total time and 4 x 3 = 12).
Therefore, the total time it will take Miguel to reach his destination is 4 hours (for the first 1/3 of the distance) + 12 hours (for the remaining 2/3 of the distance) = 16 hours.
None of the options provided matches the correct answer, as the total time should be 16 hours, not 8 hours.
To find the total time it will take Miguel to reach his destination, we can use the ratio of distance traveled to time taken.
Given that Miguel has driven 2/3 of the total distance in 4 hours, we can set up a proportion:
(2/3) distance / 4 hours = total distance / total time
To find the total time, we can cross-multiply:
(2/3) distance * total time = 4 hours * total distance
Simplifying the equation, we get:
2/3 * total time = 4
Now, let's solve for total time:
total time = (4 * 3) / 2
total time = 12 / 2
total time = 6 hours
Therefore, the total time it will take Miguel to reach his destination is 6 hours.
B: 12 hours