Unit Rates with Ratios of Fractions Quick Check
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Question
Miguel is returning from a trip. In 4 hours, he has driven 23 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?(1 point)
Responses
83 hours
Start Fraction 8 over 3 End Fraction hours
8 hours
8 hours
12 hours
12 hours
6 hours
6 hours
To find the total time it will take Miguel to reach his destination, we can set up a proportion using the information given:
4 hours = 23 of the total distance
x hours = 1 of the total distance
To solve for x, we can set up the proportion:
4/23 = x/1
Cross-multiplying, we get:
4 = 23x
Dividing both sides by 23, we find that:
x = 4/23
Therefore, at this rate, it will take Miguel 4/23 hours to reach his destination.
The correct response is:
Start Fraction 8 over 3 End Fraction hours
To solve this question, we can set up a proportion using the given information. We know that Miguel has driven 23 units of distance in 4 hours. We want to find out how long it will take him to drive the total distance, so we can set up the proportion as follows:
23 units / 4 hours = total units / total hours
To find the total units, we need to determine what the total distance is. The problem states that Miguel has driven 23 of the total distance, so we can set up another proportion:
23 units / total distance = 4 hours / total hours
Now we can solve for the total hours. Cross multiply the fractions:
23 units * total hours = 4 hours * total distance
23 total hours = 4 total distance
Divide both sides of the equation by 23 to isolate the total hours:
total hours = (4 total distance) / 23
So, at this rate, the total time it will take Miguel to reach his destination is (4 total distance) / 23 hours.
Now, the answer choices are:
A) 83 hours
B) 8 hours
C) 12 hours
D) 6 hours
Plug in the appropriate values for the total distance into the formula we derived. We don't have the total distance given in the question, so we cannot calculate an exact answer.
To find the total time it will take Miguel to reach his destination, we can set up a proportion using the given information:
4 hours corresponds to 23 of the total distance.
Let's represent the total time as T. The proportion can be written as:
4 hours / 23 distance = T hours / 1 total distance
Cross-multiplying, we get:
4 hours * 1 total distance = 23 distance * T hours
4T = 23
Dividing both sides by 4, we find that:
T = 23 / 4
Simplifying the fraction, we get:
T = 5.75 hours
Therefore, the total time it will take Miguel to reach his destination is 5.75 hours.