priya decides to go to the store which is 8km from her house. she first ran at a rate of 7km/h then walked the rest of the trip at a speed of 3km/h. if the total trip took 2hrs how many kilometers did she walk?
If she walked x km, then since time = distance/speed,
x/3 + (8-x)/7 = 2
To calculate the distance Priya walked, we need to find out the time she spent running.
Let's assume the time Priya spent running is "t" hours. Since the total trip took 2 hours, then the time she spent walking would be 2 - t hours.
We can now calculate the distances Priya ran and walked using the formula Distance = Speed × Time.
The distance Priya ran is given by: Distance Ran = Speed Ran × Time Ran = 7 km/h × t hours.
The distance Priya walked is given by: Distance Walked = Speed Walked × Time Walked = 3 km/h × (2 - t) hours.
Since the total distance Priya covered is 8 km, we can add the distances ran and walked together and set it equal to 8 km:
Distance Ran + Distance Walked = 8 km
7t + 3(2 - t) = 8
Now, we can simplify the equation:
7t + 6 - 3t = 8
4t = 2
Dividing both sides of the equation by 4:
t = 0.5
So, Priya spent 0.5 hours running and the remaining 1.5 hours walking.
To calculate the distance Priya walked, we can substitute the value of t into the distance formula:
Distance Walked = Speed Walked × Time Walked
Distance Walked = 3 km/h × 1.5 hours
Distance Walked = 4.5 km
Therefore, Priya walked 4.5 kilometers.