Question

1. rick and mark drove boats on the lake for the same amount of time. rick’s average speed was 10 mph and mark’s was 14 mph. if mark traveled 8 miles further than rick, how much time were they both on the lake?

Explanation:

Step1: Set up the distance - speed - time equations

Let the time they were on the lake be $t$ hours. Distance $d = vt$ (where $v$ is speed and $t$ is time). Rick's distance $d_{1}=10t$, Mark's distance $d_{2} = 14t$.

Step2: Use the given distance relationship

We know that Mark traveled 8 miles further than Rick, so $d_{2}-d_{1}=8$. Substitute $d_{1}=10t$ and $d_{2}=14t$ into the equation: $14t - 10t=8$.

Step3: Simplify and solve for $t$

Combine like - terms: $4t = 8$. Divide both sides by 4: $t=\frac{8}{4}=2$.

Answer:

2 hours