Proportions and equal problems

Question

At 10 am a snowstorm is 250 miles west of St.Louis. The storm travels 150 miles eastward at a constant rate, and then it’s speed decreases by 5 miles per hour. If the storm reaches St.Louis at 8.00 P.M., what was the storm’s original speed?

Answer 1

Let R = original rate then R-5 = decreased rate

150/R = time at original rate

100/(R-5) = time at reduced rate

(150/R) + [100/(R-5)] = 10

Divide by 10 and multiply through by R(R-5)

15(R-5) + 10R = R(R-5)

15R - 75 + 10R = R² - 5R

R² - 30R + 75 = 0

The quadratic formula gives only one sensible root, i.e. R=27.24745