On a certain day it took Bill three times as long to drive from home

On a certain day it took Bill three times as long to drive from home to work as it took Sue to drive from home to work. How many kilometers did Bill drive from home to work?

{Bill's Time} = 3*{Sue's Time}

(1) Sue drove 10 kilometers from home to work, and the ratio of distance driven from home to work time to drive from home to work was the same for Bill and Sue that day.

Sue's distance = 10km,

The ratio of distance to time is rate of speed, so we are told that Bill's speed is the same as Sue's. As Bill's time was three times longer, with the same rate he would cover 3 times more distance than Sue did.

{Bill's distance} = 3*{Sue's distance} = 3*10 = 30km.

Sufficient.

(2) The ratio of distance driven from home to work time to drive from home to work for Sue that day was 64 kilometers per hour. Only rate of Sue is given. Not sufficient.

Answer: A.
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thank you Bunuel....but am I wrong to assume that they may have driven the same distance, however, Bill just took a longer time?! That was why I got stuck in asnwering the question. ANy advice you offer will be appreciated.

Let's do this algebraically:

Bill's Time =3* Sue's Time --> \(Bt=3*St\)

(1) Sue's distance 10km --> \(Sd=10\)

\(\frac{Sd}{St}=\frac{Bd}{Bt}\) -->

\(\frac{10}{St}=\frac{Bd}{3*St}\) -->

\(Bd=30\)

As for your question: statement 1 tells us that Bill's and Sue's rates are the same, and Bill spent 3 times more time to cover his distance. Obviously distances can not be the same if rates are same and time are not as Distance=Time*Rate.

Hope it's clear.
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