SOLUTION: in six hours A walks 10 kilometers more than B in five hours and in 8 hours B walks 7 kilometers more than A does in 5 hours what are the speeds of each person?

Question 998576: in six hours A walks 10 kilometers more than B in five hours and in 8 hours B walks 7 kilometers more than A does in 5 hours what are the speeds of each person?
Found 2 solutions by fractalier, stanbon:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call their rates A and B. The equations become (since rate times time = distance):
6A - 5B = 10
8B - 5A = 7 (or -5A + 8B = 7)
Now solve this system of equations...multiply appropriately to get
30A - 25B = 50
-30A + 48B = 42
When we add these we get
23B = 92 and
B = 4 km/hr
A can be found by substituting into the first equation
6A - 5(4) = 10
6A = 30
A = 5 km/hr
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
in six hours A walks 10 kilometers more than B in five hours and in 8 hours B walks 7 kilometers more than A does in 5 hours what are the speeds of each person?
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6a = 5b+10
8b = 5a+7
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Rearrange::
6a - 5b = 10
5a - 8b = -7
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Modify for elimination::
30a - 25b = 50
30a - 48b = -42
-------------------
Subtract and solve for "b"::
23b = 92
b = 4 km/hr (B's rate)
-----
Solve for "a":
6a - 5b = 10
6a - 20 = 10
6a = 30
a = 5 km/hr (A's rate)
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Cheers,
Stan H.
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