Willie Fennish participated in the 40 mile "Iron Man" challenge. He spent a fourth of the time swimming at 5mph, a third of the time on a bicycle at 15mph, and the rest of the time running at 10 mph. How long did it take for Willie to finish the race? (nearest minute)
How would I set up this equation?
Let the total time taken be $t$. Then we have that $\frac{1}{4}t$ is the time he swam, $\frac{1}{3}t$ is the time he biked, and $\frac{5}{12}t$ is the time he spent running. We know that the total distance is $40$ as well as the velocities involved in each segment of the race. Using the equation $d=vt$, we get $40=\Sigma \,vt\rightarrow 40=\frac{5}{4}t+\frac{15}{3}t+\frac{50}{12}t$. You can just solve that for $t$. (I'm just multiplying the time taken in each segment of the race by the velocity at which the racer completed that segment.)