SOLUTION: Rico can drive 2 times as fast as Luis can ride his bicycle. If it takes Luis 2 hours longer than Rico to travel 88 miles, how fast can Luis ride his bicycle?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Rico can drive 2 times as fast as Luis can ride his bicycle. If it takes Luis 2 hours longer than Rico to travel 88 miles, how fast can Luis ride his bicycle?      Log On


   

Question 994108: Rico can drive 2 times as fast as Luis can ride his bicycle. If it takes Luis 2 hours longer than Rico to travel 88 miles, how fast can Luis ride his bicycle?
Found 3 solutions by josgarithmetic, MathTherapy, addingup:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
RT=D uniform rate equation to relate speed (rate), time, and distance. 
           speed      time     distance
Rico       nr          t        d
Luis        r          t+k      d

system%28n=2%2Ck=2%2Cd=88%2Cr=unknownSpeed%2Ct=unknownTime%29

Symbolic System To Solve for variables r and t:
system%28nr%2At=d%2Cr%28t%2Bk%29=d%29


More than one way to solve this, but most pleasant may be,...
t=d%2F%28nr%29
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rt%2Bkr=d
r%28d%2F%28nr%29%29%2Bkr=d
d%2Fn%2Bkr=d
kr=d-d%2Fn
r=d%2Fk-d%2F%28kn%29
r=dn%2F%28kn%29-d%2F%28kn%29
highlight%28r=%28dn-d%29%2F%28kn%29%29--------this may be the most comfortable formula for r to use, but which form you use for evaluation is your choice.
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Maybe use as highlight%28r=d%28n-1%29%2F%28kn%29%29

SUBSTITUTION
r=88%282-1%29%2F%282%2A2%29
r=22

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Rico can drive 2 times as fast as Luis can ride his bicycle. If it takes Luis 2 hours longer than Rico to travel 88 miles, how fast can Luis ride his bicycle?
Let Luis’ speed be S

Then Rico’s speed = 2S

We then get the following time equation: 88%2FS+=+88%2F%282S%29+%2B+2

176 = 88 + 2(2S) ------- Multiplying by LCD, 2S

176 = 88 + 4S

176 – 88 = 4S

88 = 4S

S, or Luis’ speed = 88%2F4, or highlight_green%2822%29 mph

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
R - time for Rico to drive 88 miles
L - time for Luis to bike 88 miles
R can drive 2 times faster, which means he will get to the end in 1/2 the time
Now we have an equation:
R=1/2L
Also, it took Luis 2 hours longer than Rico:
R+2=L
Now, on this last equation let's substitute tha value of R:
1/2L+2= L Subtract 1/2L from both sides
2= 1/2L Now divido both sides by 1/2
4= L, or L= 4 So it takes Luis 4 hours to do the 88 miles. Finally:
v= d/t= 88/4= 22 miles per hour is Luis' speed