Fred runs 6 miles per hour swims 1 mile per hour and bikes 1

Fred runs 6 miles per hour, swims 1 mile per hour, and bikes 10 miles an hour. He finished a triathlon (which requires all three events of running, swimming, and biking) in 7 hours and 42 minutes. Sam, a friend, who runs 8 miles per hour, swims 2 miles per hour, and bikes 15 miles per hour finished the triathlon course in 5 hours and 30 seconds. The total course was 49 miles long. How many miles was each segment (running, swimming, and biking) of the triathlon? Use any of the concepts in the first three chapters to solve this problem; the method of guess-and - check will not be acceptable way to solve this problem for this quiz. Show, in detail, how you arrived at your answer. If you are wondering, yes, the times above are correct; the first time is in hours and minutes and the second time is in hours and seconds! The solution to this problem is worth 5 points.

Solution

Let x miles is running , y miles is swimming and z miles is biking

So, Fred x/6 + y/1 + z/10 = 7.7 ----(1)

Sam : x/8 + y/2 + z/15 = 5.008 ----(2)

x +y + z = 49 -----(3)

We have three equations to solve for x , y , z