Bunuel wrote:

Cecile commutes from her home to her office by either driving her car or riding her bike. If she drives, she covers one mile in 4 minutes and and if she rides her bike she cover one mile in 9 minutes. If it takes her 30 minutes longer to ride her bike from her home to her office than to drive, how far is the distance from her home to her office?

A. 5 miles

B. 6 miles

C. 8 miles

D. 9 miles

E. 12 miles

Let Distance be D.

Speed of car = \(\frac{1}{4}\) miles/min

Let Time taken by car = t

Speed of bike = \(\frac{1}{9}\) miles/min

Time taken by bike = 30 mins longer than time taken by car = t + 30

\(D = \frac{1}{4} * t\) -------- (i)

\(D = \frac{1}{9}* (t + 30)\) ------------- (ii)

Equating (i) and (ii), we get;

\(\frac{1}{4} * t = \frac{1}{9} * (t + 30)\)

\(\frac{t}{4} = \frac{(t + 30)}{9}\)

\(9t = 4t + 120\)

\(5t = 120\)

\(t = 24\)

Substituting value of t in (i), we get;

\(D = \frac{1}{4} * 24 = 6 miles\).

Answer

(B)