Question 581243
Leah and Rain travel 2km to the aquatic center.
 Leah rides her bike while Rain rides an electric scooter.
 Leah's average speed is 1km/h greater than Rain's.
 Leah arrives at the center 10 min before Rain.
 What is Rain's average speed on her scooter?
:
Let r = Rain's speed on the scooter
then
(r+1) = Leah's speed on the bike
:
Change 10 min to hrs; 10/60 = {{{1/6}}} hr
:
Write a time equation; time = dist/speed
:
Rain's time - Leah's time = 10 min
{{{2/r}}} - {{{2/(r+1)}}} = {{{1/6}}}
multiply by 6r(r+1), to clear the denominators, results:
2*6(r+1) - 2(6r) = r(r+1)
:
12r + 12 - 12r = r^2 + r
12 = r^2 + r
0 = r^2 + r - 12
Factors to
(r+4)(r-3) = 0
the positive solution is what we want here
r = 3 km/h is Rain's speed
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;
:
Check this out
{{{2/3}}} - {{{2/4}}} =
{{{8/12}}} - {{{6/12}}} = {{{2/12}}} which is {{{1/6}}} of  mile