Question

If Dr. Suzuki rides his bike to his office, he averages 6 miles per hour. If he drives his car, he averages 18 miles per hour. His time driving is 1/2 hour less than his time bicycling. How far is his office?

Answer 1

dr suzuki should drive faster

Answer 2

v=d/t

Answer 3

6*t+0.5=d
18*t=d

Answer 4

solve for d, 2 equations 2 unknowns, linearly independant

Answer 5

oh sorry umm its 6(t+0.5)=d

Answer 6

Alternative formulation: let \(x\) be distance to office:

Time on bike = \(x/6\)
Time in car = \(x/18\)
Time in car = time on bike - 1/2
\[\frac{x}{18} = \frac{x}{6}-\frac{1}{2}\]Multiply by 18 to clear fractions
\[x = 3x - 9\]

Answer 7

Speed of bike (b) = 6 miles/hr
Speed of car (c) = 18 miles/hr
Distance between home to office = d

Formula: Time = Distance/Speed

Time taken by bike = d/6
Time taken by car = d/18

Car takes 1/2 hours less than a bike.

\[\frac{ d }{ 6 }- \frac{ d }{ 18 }=\frac{ 1 }{ 2 } \\ \\ \frac{ 3d }{ 18 }- \frac{ d }{ 18 }= \frac{ 1 }{ 2 }\\ \\ \frac{ 2 }{ d }= \frac{ 1 }{ 2 } \\ \\ 2d = 9 \\ \\ d = 9/2 \ miles\]

So, Dr. Suzuki's office is 9/2 (or 4.5) miles away.