SOLUTION: 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?

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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