Luisa travels 25 km in 3hours 45 mins. She walks part of the way at 4 km/h and cycles the rest at 12 km/h. How far did she walk?
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To find out how far Luisa walked, we need to determine the distance covered during each part of her journey.
Let's start by converting the time of 3 hours 45 minutes into hours:
45 minutes is equal to 45/60 = 0.75 hours.
So, the total time of Luisa's journey is 3 hours + 0.75 hours = 3.75 hours.
Now, let's calculate the distance Luisa covered at each speed.
Distance covered while walking:
Walking speed = 4 km/h
Time spent walking = 3.75 hours
Distance walked = Speed × Time
Distance walked = 4 km/h × 3.75 hours
Distance walked = 15 km
Therefore, Luisa walked a distance of 15 km.
To find out how far Luisa walked, we can calculate the time it took for her to cycle the remaining distance and subtract it from the total time.
Firstly, let's convert 3 hours and 45 minutes to a single unit, which is hours. Since there are 60 minutes in an hour, we can convert 45 minutes into hours by dividing it by 60:
45 minutes ÷ 60 minutes/hour = 0.75 hours.
Adding this to the 3 hours, we get a total time of:
3 hours + 0.75 hours = 3.75 hours.
Now, we can calculate the time taken for Luisa to cycle the distance. Since she walks part of the way at 4 km/h, the remaining distance must have been traveled at 12 km/h. We can determine the time taken for the cycling portion by using the formula:
Time = Distance / Speed
Let's denote the distance walked by 'x' km. Then the remaining distance cycled is given by:
Total Distance - Distance Walked = (25 km - x km) = (25 - x) km.
The time taken for cycling is:
Time for Cycling = (25 - x) km / 12 km/h.
Now we can express the total time Luisa took for her journey as the sum of the time taken for walking and cycling:
Total Time = Time for Walking + Time for Cycling.
Substituting the values we obtained:
3.75 hours = x km / 4 km/h + (25 - x) km / 12 km/h.
To solve this equation, we can multiply both sides by the least common multiple (LCM) of the denominators (3) to eliminate the denominators:
3.75 hours * 3 = x km / 4 km/h * 3 + (25 - x) km / 12 km/h * 3.
11.25 = 3x/4 + (25 - x)/4.
Now, we can simplify the equation:
11.25 = (3x + (25 - x)) / 4.
To eliminate the fractions, we can multiply both sides of the equation by 4:
11.25 * 4 = 3x + (25 - x).
45 = 3x + 25 - x.
45 - 25 = 3x - x.
20 = 2x.
2x = 20.
Divide both sides by 2:
x = 20 / 2.
x = 10.
Therefore, Luisa walked 10 km.
walked for t hours
times are t and 3.75-t
4 t + 12(3.75-t) = 25
-8 t = 25 - 45 = -20
t = 5/2
d = 4 (5/2) = 10 km