Question

A marathon runner runs at the rate of 9 mph for the complete course. A track man runs at 12 mph. If together they run for 3 hrs., 1 min. to complete a total of 28 miles, how far did the marathon runner run? 24 3/5 miles 21 miles 20 4/5 miles

Answer 1

The first thing to do is organize all the given data so that you won't be confused which is which. Let's denote all the given that belongs to the marathon runner with a subscript of 1 and that of the trackman with a subscript of 2. The first equation we could do is find the sum of time:

t₁ + t₂ = 3 hours and 1 minute

For consistency, let's convert minute to hours. 
1 minute (1 hour/60 minutes) = 1/60
Total time = 3+1/60 = 3.0167 hours

t₁ + t₂ = 3.0167 hours  ----> equation 1

The other equation is the total distance. When you multiply speed with time, the answer would be distance. Thus.

9t₁ + 12t₂ = 28 miles ----> equation 2

Since there are two unknowns and 2 equations, the system is solvable:

t₁ = 3.0157 - t₂
9(3.0167 - t₂) + 12t₂ = 28
t₂ = 0.2832 hour, and 
t₁ = 3.0157 -  0.2832 = 2.733 hours

Therefore, the distance run by the marathon runner is
9*2.733 = 24.597 or approximately 24 3/5.

Answer 2

Answer:

24 3/5

Step-by-step explanation: