Question 1027306: Joan averages 10 miles per hour riding her bike to town. Averaging 30 miles per hour by car takes her 2 hours less time. how far does she travel to town?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
when r = rate and t = time and d = distance, this formula becomes:
r * t = d
when r = 10 miles per hour, the formula becomes:
10 * t = d
when r = 30 miles per hour and t is 2 less, the formula becomes:
30 * (t-2) = d
you have 2 equations that need to be solved simultaneously.
those equations are:
10 * t = d
30 * (t-2) = d
subtract the second formula from the first formula and you get:
10 * t - 30 * (t-2) = 0
simplify to get:
10 * t - 30 * t + 60 = 0
combine like terms to get:
-20 * t + 60 = 0
add 20 * t to both sides of the equation and you get:
60 = 20 * t
solve for t to get:
t = 3 hours.
t-2 = 1 hour.
when she bikes at 10 miles per hour, it takes her 3 hours.
r * t = d
10 * 3 = 30 miles.
when she drives at 30 miles per hour, it takes her 1 hour.
30 * 1 = 30 miles.
it's the same distance of 30 miles as it should be.
the solution is that she travels 30 miles to town.
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