# Algebra

A man drove his automobile to New York, a distance of 550 miles, at a certain average rate. He returned from New York at the rate of 11 mph more. The entire trip required 22.5 hours. What were his rates returning and going?

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1. first rate ---- x mph
return rate --- x+11

sum of times = 22.5
550/x + 550/(x+11) = 22.5
times x(x+11)
550x + 6050 + 550x = 22.5x(x+11)
1100x + 6050 = 22.5x^2 + 247.5x
22.5x^2 - 852.5x - 6050 = 0
using the formula
x = 44 or a negative

he went at 44 mph going there, and 55 mph coming back

check:
550/44 + 550/55 = 22.5 , YEAHH

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