Indira and Jean begin their hike at 10 a.m. one morning. They plan to hike from the 2 2/5-mile marker to the 8 1/10-mile marker along the trail. They plan to hike at an average speed of 3 miles per hour. Will they reach 8 1/10-mile marker by noon? Explain your reasoning.
I had tried to add 8 1/10 and 2 2/5 then divide the sum by 3. 10 am? How do i do this please help asap. Due tomorrow!
-BoloHead Student
Let's convert these fractions to decimals.
They start at the 2.4 marker and end at the 8.1 marker
8.1 - 2.4 = 5.7 miles
5.7 / 3 = 1.9 hours
10 + 1.9 = 11.9 which is before noon.
I dunno sorry
Hard
11.9 and that means that they will be there by noon or before noon
I don't go to Pines but my math book had this problem in it. 😐
To determine if Indira and Jean will reach the 8 1/10-mile marker by noon, we can follow these steps:
1. Calculate the total distance they need to hike. To do this, we subtract the starting point (2 2/5 miles) from the ending point (8 1/10 miles):
8 1/10 - 2 2/5
To subtract mixed numbers, you need to find a common denominator, which in this case is 10. Convert both mixed numbers to improper fractions:
8 1/10 = 8 + 1/10 = 80/10 + 1/10 = 81/10
2 2/5 = 2 + 2/5 = 10/5 + 2/5 = 12/5
Now subtract the fractions:
81/10 - 12/5
To subtract fractions, they need to have a common denominator. In this case, multiply the denominators:
10 * 5 = 50
Now, adjust the fractions to have the common denominator:
(81/10) * (5/5) = 405/50
(12/5) * (10/10) = 120/50
We can now subtract the fractions:
405/50 - 120/50 = 285/50
Simplify the fraction if necessary:
285/50 = 57/10
So the total distance they need to hike is 57/10 miles.
2. Calculate the time it will take them at an average speed of 3 miles per hour. To do this, divide the total distance (in miles) by the average speed (in miles per hour):
(57/10) ÷ 3
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(57/10) * (1/3)
Multiply the numerators and denominators:
(57 * 1) / (10 * 3) = 57/30
Simplify the fraction if necessary:
57/30 = 19/10
So it will take them 19/10 hours to complete the hike.
3. Determine if they will reach the 8 1/10-mile marker by noon. Since the hike starts at 10 a.m., noon is 2 hours later. We need to compare the time it takes them to hike (19/10 hours) to the 2-hour time frame.
Convert 2 hours to an improper fraction:
2 hours = 2/1
Now, compare the fractions:
19/10 > 2/1
Since 19/10 is greater than 2/1, it means they will not reach the 8 1/10-mile marker by noon.