Bill and Sam both rode their bikes from their school to the public library. They traveled the exact same route. It took Bill 12 minutes. How long did it take Sam?
(1) Sam’s average speed was 80% of Bill’s.
(2) The distance from the school to the library is two miles.
I thought I had the correct answer here with needing both pieces of information but Kaplan
explains you only need statement 1...Can anyone explain this one to me? I know they both travel the same distance but that distance could be 1 mile or 20 miles which would change Sam's travel time correct?
Both travel a distance ---call it D. Bill took 12 minutes, and Sam took a time --- call it T. Bill traveled at speed VB and Sam traveled at speed VS.
D = RT for each person ----
For Bill: D = (VB)*12
For Sam: D = (VS)*T
Since these both equal the same distance, we can equate them. (VB)*12 = (VS)*T
Now, statement #1 says ---- "Sam’s average speed was 80% of Bill’s.
" In math, VS = 0.8*VB. Plug this into the purple equation ---
(VB)*12 = [0.8*VB]*Tdivide by VB
12 = 0.8*Tdivide by 0.8
T = 12/0.8 = 15
It took Sam 15 minutes. Statement #1, alone and by itself, was sufficient for answering the prompt question.
As a general rule, if two people or cars travel the same distance, then their velocities are inversely proportional
to the times it takes them. If, starting from one speed, you multiply by something to get the second speed --- then whatever you multiplied
the speed by, you need to divide
the time by that same factor.
Does all this make sense?
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