ali walks for 1 hour at x km per hour and then for 2 hours at ( x + 1/4) km/h. he walked a total distance of 8km. write an equation and solve it to find the value of x

Question

ali walks for 1 hour at x km per hour and then for 2 hours at ( x + 1/4) km/h. he walked a total distance of 8km. write an equation and solve it to find the value of x

Answer 1

Step 1: Find the equation.

Ali walked a total distance of 8km over 3 hrs.

The first hour he walked at x km per hour. The next two hours he walked at (x + 1/4) km per hour.

This means the first hour can be interpreted as:

1hr * x km/hr

The second hour can be interpreted as:

2hr * (x + 1/4) km/hr

so if we add the first hour with the subsequent 2 hours, it should total 8km:

1hr * x km/hr + 2hr * (x + 1/4) km/hr = 8km

The hrs on the left side of the equation can cancel out because for each instance there is one in the numerator and one in the denominator. Simplifying the equation further:

1*x km + 2(x + 1/4) km = 8km

If you divide both sides of the equation by km, km cancels out. Simplifying the equation:

answer: x + 2(x + 1/4) = 8

Step 2: Solve for x

first let's break out the parenthesis by multiplying the x and 1/4 by the 2:

x + 2*x + 2/4 = 8

we can clean up a little by simplifying the fraction:

x + 2x + 1/2 = 8

x + 2x + 0.5 = 8

Now the goal is to leave the x on one side and the numbers on the other. So we can subtract 0.5 from both sides:

x + 2x + 0.5 - 0.5 = 8 - 0.5

x + 2x = 7.5

Almost there, we can simplify the equation further by adding the x's:

3x = 7.5

Lastly, divide both sides by 3 in order to leave the x by itself:

3x/3 = 7.5/3

answer: x = 2.5

Step 3: Check to make sure your answer is correct

Simply plug in the value of x found in step 2 in the equation found in step 1:

equation: x + 2(x + 1/4) = 8

x + 2(x + 0.24) = 8

plug in x and solve:

(2.5) + 2(2.5 + 0.25) = 8

2.5 + 2*2.5 + 2*0.25 = 8

2.5 + 5 + 0.5 = 8

8 = 8

Both sides of the equation are the same, so we know our answer is correct!