SOLUTION: Two hikers start walking in opposite directions from the same place at the same time. The hiker heading west is walking 2 kilometers per hour faster than the hiker heading east. If

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Question 886239: Two hikers start walking in opposite directions from the same place at the same time. The hiker heading west is walking 2 kilometers per hour faster than the hiker heading east. If they are 15 kilometers apart after 1.5 hours what is the rate of each hiker? Let x represent the rate of the westbound hiker and let y represent the rate of the eastbound hiker.
Found 2 solutions by JulietG, nerdybill:
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
Distance per hour = 15 km/1.5 kmh, or 10 kmh
X + Y = 10
Y = X + 2 (he is slower by 2)
Substitute the known value of Y from the second equation into the first.
X + Y = 10
X + (X+2) = 10
2X + 2 = 10
2X = 8
X = 4
The slower hiker is traveling 4kmh. Therefore the faster hiker is traveling 6khm.
.
Prove it:
Hiker X travels 4 * 1.5 hours, or 6 km
Hiker Y travels 6 * 1.5, or 9 km
6 + 9 = 15 km in 1.5 hours
Success!

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Two hikers start walking in opposite directions from the same place at the same time. The hiker heading west is walking 2 kilometers per hour faster than the hiker heading east. If they are 15 kilometers apart after 1.5 hours what is the rate of each hiker? Let x represent the rate of the westbound hiker and let y represent the rate of the eastbound hiker.
.
Let x = rate of westbound hiker
and y = rate of eastbound hiker
.
From: "The hiker heading west is walking 2 kilometers per hour faster than the hiker heading east."
x = y+2 (equation 1)
From: "they are 15 kilometers apart after 1.5 hours" we have
1.5(x+y) = 15 (equation 2)
substitute value of x from equation 1 into equation 2:
1.5(x+y) = 15
1.5(y+2+y) = 15
1.5(2y+2) = 15
2y+2 = 10
2y = 8
y = 4 kph (rate of eastbound hiker)
.
rate of westbound hiker:
x = y+2
x = 4+2
x = 6 kph