A women drives her snowmoble 150 miles at the rate of r mph

A women drives her snowmoble 150 miles at the rate of r mph. She could have gone the same distance in 2 hours less time if she had increased her speed by 20 mph. Find r

Solution

Actual DATA:
distance = 150 miles ; rate = r mph ; time = 150/r hrs.
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Option DATA:
distance = 150 miles ; rate = r+20 mph ; time = 150/(r+20) hrs.
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Equation:
actual time - option time = 2 hrs.
150/r - 150/(r+20) = 2
150*20 = 2r(r+20)
2r^2 + 40r - 20*150 = 0
r^2 + 20r - 1500 = 0
(r+50)(r-30) = 0
Positive solution:
rate = 30 mph (Actual driving rate)