SPEED       TIME      DISTANCE
SKATE          r           t          12
BIKE          2r          t-2         12

Let time taken to ride home, be T

Then time taken, by skateboard = T + 2

We then get the following SPEED equation:  ======> 

   24T = 12(T + 2) -------- Cross-multiplying

12(2T) = 12(T + 2)______12(2T) = 12(T + 2)

    2T = T + 2_____2T - T = 2

Time taken to ride home, or T =  

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
 .

Reena rode her skateboard to her uncle's house, 12 miles away. A wheel broke just as she arrived, so Reena borrowed 

her uncle's bicycle to return home. Traveling by bicycle, she was able to go twice as fast, and returned home in 2 hours less time 

than it took to go to her uncle's house. How long did it take Reena to get home on the bicycle?

~~~~~~~~~~~~~~~~~~~~~





More short and straightforward solution:





Let   s = her speed skateboarding to uncle's house
Then 2s = her speed biking home

Let   t = time in hrs to skateboard to uncle's house
Then  t - 2 = time in hrs to return home by bike

The distance to there d = st.
The distance back     d = 2s*(t-2).

The distance is the same:  st = 2s*(t-2)   --->  cancel the factor s in both sides  --->

t = 2(t-2)  -->  t = 2t - 4  --->  t = 4.

Thus the time skateboarding is 4 hours.

Hence, the time bicycling is 4 - 2 = 2 hours.




 

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