Problema Solution
If Dr. Susike rides his bike to his office, he averages 9 miles per hour. If he drives his car, he averages 36 miles per hour. His driving is 1/3 hour less than his time bicycling. How far is his office?
Answer provided by our tutors
Let 'S' be the distance to this office. We need to find S.
Let v1 = 9 miles/hour is the speed of his bike and 't1' be the time he needs to get to the office (pass the distance S).
Then for the distance we have S = v1 * t1
Let v2 = 36 miles/hour is the speed of his car and 't2' be the time he needs to get to the office (pass the distance S).
Then for the distance we have S = v2 * t2
Thus we can write v1 * t1 = v2 * t2 that is
9 * t1 = 36 * t2
t1 = (36 * t2) / 9
t1 = (36 / 9) * t2
t1 = 4 * t2 ........(1)
From the condition of the problem we have:
t2 = t1 - 1/3
Lets substitute t1 with 4 * t2 (from equation (1)) we will get:
t2 = 4 * t2 - 1/3
4 * t2 - t2 = 1/3
3 * t2 = 1/3
t2 = (1/3)/3
t2 = 1/9 hours
So, for the distance S = v2 * t2 = 36 * (1/9) = 4 miles.
The office of Dr. Susike is 4 miles far from his home.