Miguel is retiring 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?
Options:
6 hours
8/3 hours
12 hours
8 hours
If Miguel has driven 2/3 of the total distance in 4 hours, then the remaining 1/3 of the distance will take him the same amount of time.
So, the total time it will take him to reach his destination will be 4 + 4 = <<4+4=8>>8 hours.
Therefore, the correct option is 8 hours.
To find the total time it will take Miguel to reach his destination, we need to find the remaining time based on the portion of the distance he has already covered.
We know that in 4 hours, he has driven 2/3 of the total distance. This means that in 1 hour, he would cover 2/3 divided by 4.
To find the time it will take him to reach his destination, we need to find the remaining portion of the distance he still needs to cover. Since he has already driven 2/3, the remaining portion would be 1 - 2/3, which is 1/3.
Now, we can find the time it will take him to cover 1/3 of the total distance. Since in 1 hour he covers 2/3 divided by 4, in the same way, he would cover 1/3 divided by (2/3 divided by 4).
Calculating this, we have:
(1/3) ÷ (2/3 ÷ 4) = (1/3) × (4 ÷ 2/3) = (1/3) × (4 × 3/2) = (1/3) × (12/2) = (1/3) × 6 = 2.
Therefore, the remaining time it will take Miguel to reach his destination is 2 hours.
Adding the initial 4 hours, the total time it will take him to reach his destination is 4 + 2 = 6 hours.
Thus, the correct option is 6 hours.
To find the total time it will take Miguel to reach his destination, we first need to determine the time it takes him to drive 1/3 of the total distance.
Miguel has driven 2/3 of the distance in 4 hours. We can divide the 2/3 by 4 to find the rate at which he is driving per hour:
2/3 / 4 = 2/3 * 1/4 = 1/6
Therefore, Miguel is driving at a rate of 1/6 of the total distance per hour.
Since he has already driven 2/3 of the distance, he has 1/3 remaining. We can multiply the remaining distance by the rate to find the time it will take him to complete the trip:
1/6 * 1/3 = 1/18
So, Miguel will take 1/18 of an hour to drive the remaining 1/3 of the distance.
Finally, we need to convert this time to hours. Since there are 60 minutes in an hour, and 1/18 of an hour is equivalent to x minutes, we can set up the proportion:
1/18 = x/60
By cross-multiplication, we find:
18x = 60
x = 60/18 = 10/3
Thus, it will take Miguel 10/3 hours to reach his destination.
Therefore, the answer is the option "8/3 hours".