Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir?
To find out how long after Chris begins riding his bike, he catches up to Samir, we need to compare the distance traveled by both of them.
Let's break down the problem:
1. Samir begins riding his bike at a rate of 6 mph. We know Samir's speed, which is 6 mph.
2. Twelve minutes later, Chris leaves from the same point. So, we need to convert 12 minutes into hours. Since there are 60 minutes in an hour, dividing 12 minutes by 60 will give us the time in hours. Hence, 12 minutes is equal to 12/60 = 0.2 hours.
3. Chris bikes along the same route at 9 mph. So, Chris' speed is 9 mph.
Now, let's calculate the time it takes for Chris to catch up to Samir:
Let t represent the time (in hours) it takes for Chris to catch up to Samir.
Distance traveled by Samir, Ds = 6t
Distance traveled by Chris, Dc = 9(t-0.2)
Since they meet at the same point, the distance traveled by Samir and Chris should be equal when Chris catches up. Hence, we can set up an equation:
6t = 9(t-0.2)
Now, let's solve the equation to find the value of t:
6t = 9t - 1.8 (distributing 9 to t and -0.2)
-3t = -1.8 (subtracting 6t from both sides)
t = (-1.8) / (-3)
t = 0.6
Therefore, Chris catches up to Samir 0.6 hours after he begins riding.
To convert this time into minutes, multiply by 60:
0.6 * 60 = 36 minutes
So, Chris catches up to Samir 36 minutes after he starts riding.
can you be more specific
d1 = r*t = 6mi/h * (12/60)h = 1.2 Miles
head start.
d2 = d1 + 1.2 mi.
9t = 6t 1.2. Solve for t in hours.
1 = r*t = 6mi/h * (12/60)h = 1.2 Miles
head start.
d2 = d1 + 1.2 mi.
9t = 6t 1.2. Solve for t in hours.