james and hannah both run 4km race.james runs 1km faster than hannah and finished a quater kilometer ah head of her.how long did james run in 4km
plz show step!
To find out how long James ran in the 4km race, we can break down the information given into a step-by-step solution:
Step 1: Set up variables
Let's assume the distance that Hannah ran in kilometers is 'x.' Since James ran 1km faster than Hannah, James's distance would be 'x + 1.'
Step 2: Calculate the quarter kilometer difference
The problem states that James finished a quarter kilometer ahead of Hannah. So, we can set up the equation:
Distance covered by James - Distance covered by Hannah = 0.25 km
(x + 1) - x = 0.25
Step 3: Simplify the equation
Simplifying the equation:
x + 1 - x = 0.25
1 = 0.25
Step 4: Analyze the outcome
Since the equation 1 = 0.25 is not true, it means that our initial assumption was incorrect.
Step 5: Adjust the initial assumption
Let's assume that James ran 'y' kilometers and Hannah ran 'z' kilometers. Since James ran 1km faster, the updated equation becomes:
Distance covered by James - Distance covered by Hannah = 0.25 km
(y) - z = 0.25
Step 6: Analyze the new equation
Now, we have:
y - z = 0.25
Step 7: Analyze the given information
It is stated that both James and Hannah ran a 4km race. Therefore, we can write another equation:
y + z = 4
Step 8: Set up a system of equations
We have two equations based on the given information:
y - z = 0.25
y + z = 4
Step 9: Solve the system of equations
We can solve this system of equations using either substitution or elimination. Let's use elimination:
Adding the equations together, we get:
2y = 4.25
Dividing both sides by 2, we find:
y = 2.125
Step 10: Find the distance James ran in 4km
Since James ran 'y' kilometers, his distance in the 4km race would be 2.125km.
Therefore, James ran 2.125km in the 4km race.