A man walked for some distance at 8 km/h, and for an equal distance at 5 km/h. The total time he took was 13/4 hours. Find the total distance he walked. Explain your workings

13/4 = (x/8) + (x/5)

solve for x, which is half the total distance. then find 2x to get the total distance.

20

To find the total distance the man walked, we can use the formula:

Distance = Speed × Time

Let's assign variables to the distances and speeds:

Let x be the distance covered at 8 km/h,
And y be the distance covered at 5 km/h.

We are given that the total time is 13/4 hours. Therefore, we can write the equation:

Time at 8 km/h + Time at 5 km/h = 13/4

The time at 8 km/h can be calculated by using the formula:

Time = Distance / Speed

So, the time at 8 km/h is x / 8.

Similarly, the time at 5 km/h is y / 5.

Substituting these values into the equation for total time:

x / 8 + y / 5 = 13/4

To make the equation easier to work with, we can multiply through by 40 (the least common multiple of 8 and 5) to eliminate the denominators:

5x + 8y = (13/4) × 40
5x + 8y = 130

Now we have a system of equations. Since we have two equations and two variables, we can solve for x and y. We can solve it using any method we prefer, such as substitution or elimination.

To solve it using elimination, we will multiply the first equation by 5 and the second equation by 8 to eliminate the coefficients of x or y:

25x + 40y = 650
40x + 40y = 520

Next, subtract the second equation from the first equation to eliminate y:

(25x + 40y) - (40x + 40y) = 650 - 520

Simplifying, we get:

-15x = 130
x = 130 / -15
x = -8.67

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.

Let's use the equation x / 8 + y / 5 = 13/4:

(-8.67) / 8 + y / 5 = 13/4

Simplifying, we get:

-1.08 + y / 5 = 3.25

Subtracting -1.08 from both sides:

y / 5 = 3.25 + 1.08
y / 5 = 4.33

Multiplying both sides by 5:

y = 4.33 × 5
y = 21.67

Therefore, the man walked a distance of -8.67 km at 8 km/h and 21.67 km at 5 km/h. To find the total distance, we add the two distances:

Total distance = -8.67 + 21.67
Total distance = 13 km

So, the man walked a total distance of 13 kilometers.