SOLUTION: 2 cars start at the same time from towns a and b, and travel with constant but different speeds towards each other. They pass each other 70 km from town a, and continue to the oppo

Question 433362: 2 cars start at the same time from towns a and b, and travel with constant but different speeds towards each other. They pass each other 70 km from town a, and continue to the opposite town, where they turn around without stopping. The cars pass each other again 40 km from town b. What is the distance between the 2 towns?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Cars start at the same time from towns a and b, and travel with constant but
different speeds towards each other.
They pass each other 70 km from town a, and continue to the opposite town,
where they turn around without stopping.
The cars pass each other again 40 km from town b.
What is the distance between the 2 towns?
:
Let d = distance from a to b
:
First time they meet:
car 1 travels 70 km
car 2 travels (d-70)
:
Second time they meet
car 1 travels (d-70) + 40 = (d-30)
car 2 travels 70 + (d-40) = (d+30)
:
The ratio of the distances traveled by the two cars remain the same; therefore:
=
Cross multiply
70(d+30) = (d-70)(d-30)
70d + 2100 = d^2 - 30d - 70d + 2100
Subtract 2100 from both sides, arrange as a quadratic equation
d^2 - 100d - 70d = 0
d^2 - 170d = 0
Factor
d(d - 170) = 0
Two solutions
d = 0, obviously not the solution
and
d = 170 km distance between the towns
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