SOLUTION: Please help with this question. Keiko bicycles 8km/h faster than Javier. In the same time it takes Javier to bicycle 30 km, Keiko can bicycle 54 km. How fast does each bicyclist

Algebra ->  Systems-of-equations -> SOLUTION: Please help with this question. Keiko bicycles 8km/h faster than Javier. In the same time it takes Javier to bicycle 30 km, Keiko can bicycle 54 km. How fast does each bicyclist      Log On


   

Question 617107: Please help with this question.
Keiko bicycles 8km/h faster than Javier. In the same time it takes Javier to bicycle 30 km, Keiko can bicycle 54 km. How fast does each bicyclist travel?
Javier travels ___ km/h
Keiko travels ___ km/h
Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Javier's speed
Let +k+ = Keiko's speed
given:
(1) +k+=+j+%2B+8+
(2) +30%2Fj+=+54%2Fk+
----------------
Substitute (1) into (2)
(2) +30%2Fj+=+54%2F%28+j+%2B+8+%29+
(2) +30%2A%28+j+%2B+8+%29+=+54j+
(2) +30j+%2B+240+=+54j+
(2) +24j+=+240+
(2) +j+=+10+
and, since
(1) +k+=+j+%2B+8+
(1) +k+=+10+%2B+8+
(1) +k+=+18+
Javier travels 10 km/h
Keiko travels 18 km/h
check:
(2) +30%2F10+=+54%2F18+
(2) +3+=+3+
OK

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

Keiko bicycles 8km/h faster than Javier. 

Let x and (x+8) represent Javier's and Keiko's speeds respectively

Question states*** Note: D = rt or D/r = t

In the same time it takes Javier to bicycle 30 km, Keiko can bicycle 54 km.

+30%2Fx+=+54%2F%28x%2B8%29  Cross Multiplying to solve

    54x = 30x + 240

      24x = 240

        x = 240/24 =10kmph, Javier's speed.  Keiko's speed is 18kmph