Answer:
I suppose that each number is repeated 3 times, the actual question is:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Now, remember the relation:
Distance = Speed*Time
Let's define:
D1 = distance between Courtney's house and the beach.
D2 = distance between the beach and the park.
T1 = time that it took the first walk.
T2 = time that it took the second walk.
We know that the total distance Courtney walked is 8km, then:
D1 + D2 = 8km.
And we also know that the entire walk took 2 hours, then:
T1 + T2 = 2h.
We also have the equations:
D1 = 4km/h*T1
D2 = 5km/h*T2.
Then we have a system of equations:
D1 + D2 = 8km
T1 + T2 = 2h
D1 = 4km/h*T1
D2 = 5km/h*T2.
To solve this, first let's replace equations 3 and 4 in the first equation:
4km/h*T1 + 5km/h*T2 = 8km
Now we have only two equations left:
4km/h*T1 + 5km/h*T2 = 8km
T1 + T2 = 2h
Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:
T1 = 2h - T2.
Replacing this in the first equation gives:
4km/h*(2h - T2) + 5km/h*T2 = 8km
Now let's solve this for T2.
8km - 4km/h*T2 + 5km/h*T2 = 8km
8km + 1km/h*T2 = 8km
1km/h*T2 = 0
from this, we have T2 = 0
This would mean that T1 = 2h.
Then:
D1 = 4km/h*2h = 8km.
T2 = 0
D2 = 5km/h*0 = 0.
This happens because the numbers in the problem were not well thought.
You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.
