having an issue with this word problem. Jordan travels 3/4 of a mile longer to school each day than Harrison does. Combined,they travel 5 1/4 miles to school. How far does each travel?
Let n stand for the distance jordan travels.
Let's solve this word problem step-by-step.
Step 1: Assign variables to the unknowns in the problem.
Let n be the distance Jordan travels to school.
The problem states that Jordan travels 3/4 of a mile longer than Harrison, so Harrison's distance is n - 3/4.
Step 2: Write an equation based on the information given in the problem.
The problem states that combined, they travel 5 1/4 miles to school.
So, the equation is:
n + (n - 3/4) = 5 1/4
Step 3: Simplify the equation.
n + n - 3/4 = 5 1/4
2n - 3/4 = 5 1/4
Step 4: Convert the mixed numbers to improper fractions.
The fraction 5 1/4 can be rewritten as 21/4.
So the equation becomes:
2n - 3/4 = 21/4
Step 5: Solve the equation for n.
To eliminate the fractions, multiply both sides of the equation by the common denominator, which is 4.
4(2n - 3/4) = 4(21/4)
8n - 3 = 21
Next, add 3 to both sides of the equation to isolate the variable n.
8n - 3 + 3 = 21 + 3
8n = 24
Finally, divide both sides of the equation by 8 to solve for n.
n = 24/8
n = 3
Step 6: Find Harrison's distance.
Since Harrison's distance is n - 3/4, we substitute the value of n we found in step 5.
Harrison's distance = 3 - 3/4
Harrison's distance = 3 - 0.75
Harrison's distance = 2.25 miles
Step 7: Check your answer.
To check our answer, we add the distances of Jordan and Harrison.
3 + 2.25 = 5.25 miles
Since the combined distance is 5.25 miles, our answer is correct.
Therefore, Jordan travels 3 miles to school, and Harrison travels 2.25 miles to school.
To solve this problem, let's set up an equation based on the given information.
Since Jordan travels 3/4 of a mile longer than Harrison each day, we can say that the distance Jordan travels is equal to the distance Harrison travels plus 3/4 of a mile. So, we can write the equation as:
n = (distance Harrison travels) + 3/4
Next, we are told that combined, they travel 5 1/4 miles to school. This can be written as:
(distance Harrison travels) + n = 5 1/4
Now, substitute the value of n from the first equation into the second equation:
(distance Harrison travels) + (distance Harrison travels + 3/4) = 5 1/4
Combine like terms:
2(distance Harrison travels) + 3/4 = 5 1/4
Multiply the entire equation by 4 to get rid of the fraction:
8(distance Harrison travels) + 3 = 21
Subtract 3 from both sides of the equation:
8(distance Harrison travels) = 18
Divide both sides of the equation by 8:
(distance Harrison travels) = 2 1/4
Now, substitute this value back into the first equation:
n = (2 1/4) + 3/4
n = 9/4 + 3/4
n = 12/4
n = 3
So, Jordan travels 3 miles each day, while Harrison travels 2 1/4 miles each day.
had equation correct, but I thought you divided 4 2/4 by 2 and I got 2 1/2. It didn't add up.
n + n + 3/4 = 5 1/4
2n = 4 5/4 - 3/4
2n = 4 2/4
n = 2 1/4