Problem of the Week
Problem C and Solution
Hurry Up

Problem

Ethan is riding his e-scooter $6$ km to basketball practice. When he left his house he checked his watch and determined that he had $24$ minutes to get to practice. He started off at a speed of $12$ km/hr, but after $12$ min he realized he needs to increase his speed in order to get to practice on time. For the remaining time, what speed should Ethan ride at in order for the entire trip to take exactly $24$ minutes?

Solution

The entire trip is $6$ km and should take $24$ minutes. Already Ethan has traveled for $12$ min. That means the rest of his trip should take $24-12=12$ minutes.

For the first $12$ minutes, Ethan rode at $12$ km/h. This means that at that speed, in one hour, he would have traveled $12$ km. Since $12$ minutes is equal to $\frac{12}{60}=\frac{1}{5}$ of an hour, then the distance traveled during the first $12$ minutes is $\frac{1}{5}$ of $12$ km. This is $12÷5=2.4$ km. Since the total distance is $6$ km, Ethan has to travel $6-2.4=3.6$ km in the remaining $12$ min.

We need to determine the speed that Ethan should ride at to accomplish this. Ethan needs to travel $3.6$ km in $12$ min, or $\frac{1}{5}$ of an hour. At this speed, Ethan would travel $3.6\times 5=18$ km in one hour. Therefore, Ethan must ride at $18$ km/hr for the remaining time in order for the trip to take exactly $24$ minutes.