SOLUTION: DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hou

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Question 1122912: DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.

Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
d=velocity*time
D rides x mph for 0.75 hr or 0.75x for d
F rides (x+6) mph for 0.5 hr for (x/2)+3 d
0.75x+0.5x+3=23 miles, so 1.25x=20 miles
x=16 mph for D, and he rides 12 miles in 3/4 hour
x+6=22 mph for F, and he rides 11 miles in 1/2 hour.
23 miles

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = Damarcus’s distance from town
Let +s+ = Damarcus’s speed
————————
Fabian’s equation:
(1) +23+-+d+=+%28+s+%2B+6+%29%2A%281%2F2%29+
Damarcus’s equation:
(2) +d+=+s%2A%28+3%2F4+%29+
———————————-
Plug (2) into (1)
(1) +23+-+s%2A%283%2F4%29+=+%28+s+%2B+6+%29%2A%281%2F2%29+
Multiply both sides by 4
(1) +92+-+3s+=+2s+%2B+12+
(1) +5s+=+80+
(1) +s+=+16+
And
+s+%2B+6+=+22+
—————————-
Demarcus’s Speed is 16 mi/hr
Fabian’s speed is 22 mi/hr
—————-
Check:
(2) +d+=+16%2A%283%2F4%29+
(2) +d+=+12+ mi
Now check (1) by finding +d+