# Intermediate Algebra

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A car travels 30 miles in the same time that a car traveling 5 miles per hours faster travels 45 miles. What is the rate of each car?

• Intermediate Algebra -

speed of slower car --- x
speed of faster car ---- x+5

time of slower car to go 30 miles = 30/x
time of faster car to go 45 miles = 45/(x+5)
but they are the same, so ---
45/(x+5) = 30/x
45x = 30x + 150
15x = 150
x = 10

so the slow car goes 10 mph (very slow) and the faster car goes 15 mph

check:
at 10 mph, it takes 30/10 or 3 hrs to got 30 miles.
at 15 mph , to go 45 miles, takes 45/15 = 3 hrs

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