Question 830624: Two trains started from the same station at the same time and traveled in opposite directions. After traveling 10 hours, they were 850 miles apart. The rate of the faster train exceeded the rate of the slower train by 5 mph. What was the rate of the faster train?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Let a be the rate of the first train and b the rate of the second.
We're given the following:
10(a + b) = 850
a = b+5
Distribute or divide. Since it's even, I'll divide each side by 10.
(a + b) = 85
Substitute the value for a
(b+5) + b = 85
Subtract 5 from each side
B + b = 80
Add bs
2B = 80
Divide each side by 2
B = 40
Since we're told that a = b+5, a must be 45.
.
Let's prove this by adding in the values, 40 & 45
In 10 hours, train a travels 400 miles (40*10)
In 10 hours, train b travels 450 miles (45*10)
400 + 450 does indeed equal 850 miles.
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