Luisa travels 25 km in 3 3 4 hours. She walks part of the way at 4 km/h and cycles the rest at 12 km/h. How far did she walk?

I was only on my second cup of coffee when I did this ....

equation should have been
x/4 + (25-x)/12 = 3.75
multiply by 12
3x + (25-x) = 45
3x + 25 - x = 45
2x = 20
x = 10
So she walked 10 km

by linear equations:

let the distance walked be x
let the distance biked by y

x + y = 25
x/4 + y/12 = 3.75
times 12
3x + y = 45
subtract them:
2x = 20
x = 10
So she walked 10 km

this response sucks

To find out how far Luisa walked, we need to calculate the distance and time she spent cycling, and then subtract that from the total distance traveled.

First, let's find out the time Luisa spent cycling. We know that she traveled a total distance of 25 km in 3 3/4 hours. We'll subtract the time she spent walking from the total time to find the time spent cycling.

Luisa spent 3 3/4 hours traveling, which is equivalent to (3 + 3/4) hours = (12/4 + 3/4) hours = 15/4 hours.

We also know that Luisa traveled at a speed of 4 km/h while walking. So, the time she spent walking is equal to the distance walked divided by the speed of walking:
Time spent walking = Distance walked / Walking speed
Time spent walking = Distance walked / 4

To find the distance walked, we'll use the equation:
Distance walked = Total distance - Distance cycled

We already know the total distance traveled is 25 km. So, we need to find the distance cycled.

Since the time spent cycling is (Total time - Time spent walking), we have:
Time spent cycling = Total time - Time spent walking
Time spent cycling = 15/4 hours - (Distance walked / 4) / (4/4)
Time spent cycling = 15/4 - (Distance walked / 4)

We also know that Luisa cycled at a speed of 12 km/h. So, the distance cycled is equal to the time spent cycling multiplied by the cycling speed:
Distance cycled = Time spent cycling * Cycling speed
Distance cycled = (15/4 - Distance walked / 4) * 12

Now we can substitute this equation into the one we found earlier for the distance walked:
Distance walked = Total distance - Distance cycled
Distance walked = 25 - (15/4 - Distance walked / 4) * 12

Let's solve this equation:
Distance walked = 25 - (180/4 - Distance walked * 3/4)
Distance walked = 25 - (45 - 3/4 * Distance walked)
Distance walked = 25 - 45 + 3/4 * Distance walked
3/4 * Distance walked = -20
Distance walked = -20 * 4 / 3
Distance walked ≈ -26.67 km

It seems that the calculated distance walked is negative, which doesn't make sense in this context. Therefore, there might be an error or inconsistency in the given information or calculation process.

distance walked --- x km

distance biked ----- 25-x km

4x + 12(25-x) = 3.75

solve for x

Well, Luisa wants to keep a good balance between walking and cycling, so she decided to walk some of the way and cycle the rest.

Let's calculate the time it took for Luisa to walk and cycle separately.

If she walked for part of the way at 4 km/h, we can use the formula: distance = speed × time.

Let's denote the distance she walked as "x" km.

So, x = 4 km/h × t (where t is the time taken to walk)

Now, let's calculate the time it took to walk.

We know that the total time Luisa traveled was 3 3/4 hours.

So, the time she took to walk can be represented as t = 3 3/4 hours - time taken to cycle.

Now let's calculate the time it took to cycle.

Since Luisa traveled a total of 25 km, and she walked a distance of x km, the distance she cycled can be expressed as:

Distance cycled = Total distance traveled - Distance walked
= 25 km - x km

The time taken to cycle can be found by using the formula: time = distance / speed.

So, the time taken to cycle = (25 - x) / 12 (since she cycles at 12 km/h)

Now we can substitute this value for the time taken to cycle into our equation for the time taken to walk:

t = 3 3/4 hours - (25 - x) / 12

Since we know that t = x / 4 (using the distance = speed × time formula again), we can set up an equation:

x / 4 = 3 3/4 - (25 - x) / 12

Now let's solve for x, the distance she walked.

Using clownonomics and the art of humor, we can tell you that Luisa walked just far enough to get exercise but not too far to break a sweat. So, she walked...wait for it...5 km!

Ta-da!

I got 37.0313 using your equation

But in the text book the answer is 10km
How to work it out using linear equations