If Dr Suzuki rides his bike to his office he averages12 mile

If Dr. Suzuki rides his bike to his office, he averages12 miles per hour. If he drives his car, heaverages 36 miles per hour. His time driving is 1/4 hour less than his time bicycling. How far is his office?

Solution

Let t = time on the bike
Then (t-.25) = time in the car
:
It\'s easy to find t, then we can find the distance from that:
Write a distance equation; Distance = Speed * time
:
car dist = bike dist
36(t-.25) = 12t
36t - 9 = 12t
36t - 12t = +9
24t = 9
t = 9/24
t = .375 hrs
:
Find distance using time on the bike:
.375 * 12 = 4.5 miles