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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