samir begins riding his bike at a rate of 6 miles per hour. twelve minutes later, chris leaves from the same…

samir begins riding his bike at a rate of 6 miles per hour. twelve minutes later, chris leaves from the same point and bikes along the same route at 9 miles per hour. how long after chris begins riding does he catch up to samir?\n4 min\n12 min\n24 min\n40 min

samir begins riding his bike at a rate of 6 miles per hour. twelve minutes later, chris leaves from the same point and bikes along the same route at 9 miles per hour. how long after chris begins riding does he catch up to samir?\n4 min\n12 min\n24 min\n40 min

Answer

Explanation:

Step1: Convert 12 minutes to hours

Since 1 hour = 60 minutes, 12 minutes = $\frac{12}{60}=0.2$ hours. Samir has a head - start distance. Using the formula $d = vt$ (where $v$ is velocity and $t$ is time), Samir's head - start distance $d_1=6\times0.2 = 1.2$ miles.

Step2: Set up an equation for when Chris catches up with Samir

Let $t$ be the time (in hours) that Chris has been riding. Then Samir has been riding for $t + 0.2$ hours. When Chris catches up with Samir, their distances are equal. So, $6(t + 0.2)=9t$.

Step3: Expand and solve the equation

Expand the left - hand side: $6t+1.2 = 9t$. Subtract $6t$ from both sides: $1.2=9t - 6t$, which simplifies to $3t = 1.2$. Then $t=\frac{1.2}{3}=0.4$ hours.

Step4: Convert the time from hours to minutes

Since 1 hour = 60 minutes, $0.4$ hours is $0.4\times60 = 24$ minutes.

Answer:

24 min