Bunuel wrote:
Laura and Jeff plan to drive along the same route to the same destination. If it will take one hour for Jeff to travel the route, and Laura travels at a rate that is 50% faster than Jeff's rate, how long will it take Laura?
A. 30 minutes
B. 35 minutes
C. 40 minutes
D. 45 minutes
E. 50 minutes
Assign a valueJeff and Laura travel the same distance, D
We have
• a time for Jeff
• a rate for Laura in relation to Jeff
Given any distance, D, variable or assigned, we can
• find Jeff's rate and thus Laura's rate, and
• find Laura's time
Let
D = 4 miles
• Jeff's rate? Jeff drives D = 4 miles in t = 1 hour
J's
rate:
\(\frac{D}{t}=\frac{4}{1}\)= 4 mph
• L's
rate, 50% faster than J's =
\((1.5 * 4)=6\) mph
• L's
time?
\(T=\frac{D}{r}=\frac{4}{6}=\frac{2}{3}\) hour
L's time = 40 minutes
ANY fraction of an hour * 60 = minutes. So
\(\frac{2}{3}*60=40\)mins)
Answer CAlgebra (or inverse proportion)Let Jeff's rate =
\(J\)Let Laura's time =
\(t_2\)Jeff's time in minutes: 1 hour =
\(60\)(Answers are in minutes)
• Overall strategy: Use equal distance to find Laura's time
1) Find distance in terms of Jeff, D = r*t
Jeff drives at rate
\(J\) mph for 60 minutes
D in terms of Jeff =
\((r*t)=(J*60)= 60J\)2) Find distance in terms of Laura, D = r*t
Laura's rate? She drives 50% faster than Jeff
L's
rate:
\((J+\frac{1}{2}J)=\frac{3}{2}J\)L's
time =
\(t_2\)D in terms of Laura =
\((r*t)=(\frac{3}{2}J*t_2)\) 3)
D = D. Set distances equal, solve for Laura's time
\(\frac{3}{2}J * t_2 = 60J\)
So \(t_2 =\frac{60J}{(\frac{3}{2})J}=(60J*\frac{2}{3}J)=40\) minutes
Laura's time, \(t_2 = 40\) minutes
Answer C*
Note: rate and time are inversely proportional. Distances are equal.
Flip Laura's rate, \(\frac{3}{2}J\),
to get Laura's time, namely, \(\frac{2}{3}J\).
If J's time is in hours, convert L's final time to minutes. Much quicker, though perhaps not as easy to see.
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