Question

distance rate time

1. shawn and brittney rode bikes for the same amount of time. shawn traveled at 12 mph and brittney at 15 mph. if brittney traveled 16 miles further than shawn, how much time were they both riding bikes for?

Explanation:

Step1: Set up distance - rate - time equations

Let \(t\) be the time they both rode. Distance \(d = rt\) (where \(r\) is rate and \(t\) is time). Shawn's distance \(d_1=12t\) and Brittney's distance \(d_2 = 15t\).

Step2: Use the given distance relationship

We know that Brittney traveled 16 miles further than Shawn, so \(d_2=d_1 + 16\). Substituting the expressions for \(d_1\) and \(d_2\), we get \(15t=12t + 16\).

Step3: Solve for \(t\)

Subtract \(12t\) from both sides: \(15t-12t=12t + 16-12t\), which simplifies to \(3t=16\). Then \(t=\frac{16}{3}\) hours.

Answer:

\(\frac{16}{3}\) hours