On a 20 mile course, Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?

A. 75
B. 105
C. 117
D. 150
E. 162

The OA is the option C.

Experts, what is the best and fastest way to solve this PS question? Could you show me how would you solve it? Thanks in advanced.

Hi Vincen,
Let's take a look at your question.

Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes.
We can find the distance covered by Pat in the first 12 minutes by first converting 12 minutes to hours. We need to be in same units.
$$Time=\frac{12}{60}=\frac{1}{5}hours$$
We know that:
$$Distance=Speed\times Time$$
$$Distance=30\times\frac{1}{5}=6\ miles$$
$$Remaining\ Distance=20-6=14\ miles$$

He covered the rest of the distance i.e. 14 miles at an average rate of 8 miles per hour. We will now find time to cover the remaining distance.
$$Distance=Speed\times Time$$
$$14=8\times Time$$
$$Time=\frac{14}{8}=\frac{7}{4}hours$$
$$Time=\frac{7}{4}\times60\ \min=105\ \min$$

Minutes Pat took to cover the entire course = 12 + 105 = 117 minutes

Therefore, Option C is correct.
Hope it helps.
I am available if you'd like any follow up.