Brian is participating in a 345 mile endurance program that

Brian is participating in a 34.5 mile endurance program that begins with jogging and ends with biking. He jogs at 5 miles per hour to a location where he picks up his bike and rides at 18 miles per hour to the finish line. Find the amount of time he traveled at each of the speeds if his total time for the endurance program was 2 hours and 21 minutes?

Solution

21 minutes = 21/60 hours = 7/20 hours
2 hours 21 minutes = (2 + 7/20) = 47/20 hours

Let us suppose that Brian jogged for \'t\' hours.
So, he rode on bike for (47/20 - t) hours.

Distance = Speed x Time

The distance for which Brian jogged = 5t miles.
The distance for which Brian biked = 18(47/20 - t) = (42.3 - 18t) miles.
Therefore the total distance traveled = (42.3 - 13t) miles.
But this distance is equal to 34.5 miles.

So, 42.3 - 13t = 34.5
13t = 42.3 - 34.5 = 7.8
t = 7.8/13 = 0.6
So, he jogged for 0.6 hrs. i.e. for 36 minutes and biked for the rest (141 - 36 =) 105 mins i.e. 1 hr. 55 mins.