Carol started from home on a trip averaging 30 miles per hour how fast must her mother drive to catch up to her in 3 hours if she leaves 30 minutes after Carol? Use an equation to solve your work.
a.35 mph
b.39 mph
c.40 mph
I heard that the answer is a, but I don't know how to set up the equation.
carol drives for 3 hours
d = r t
d = 30 * 3 = 90 miles
mother drove 90 miles in 2.5 hours
90 = r (2.5)
t = 36 miles/hour
carol drove for 3.5 hours
d = 30*3.5 = 105 miles
mother drove 105 miles in 3 hours
105 = r(3)
r == 35
so yes a
15 represents her half hour headstart.
3 hours represents how the mother and child have to meet at the same time.
15+3(30) = 3x
15+90 = 3x
105 = 3x
35=x
Check
15+30(3) = 3(35)
105=105
To solve this problem, we can set up an equation representing the distance Carol travels and the distance her mother needs to catch up. Let's break it down step by step:
1. First, let's find out how far Carol traveled in 3 hours. We can do this by multiplying her average speed of 30 miles per hour by the time she traveled, which is 3 hours. So, Carol traveled 30 * 3 = 90 miles.
2. Now, let's find out when Carol's mother starts her journey. We know that she leaves 30 minutes (or 0.5 hours) after Carol. Since Carol has been traveling for 3 hours already, Carol's mother will only have 3 - 0.5 = 2.5 hours to catch up.
3. Now, let's represent the distance Carol's mother needs to catch up to Carol using the equation: Distance = Speed * Time. Let's call Carol's mother's speed "S." The distance Carol's mother needs to travel is the same as the distance Carol traveled, which is 90 miles.
Therefore, the equation is: 90 miles = S * 2.5 hours.
4. Now, we can solve the equation for the speed S. Divide both sides of the equation by 2.5: 90 miles / 2.5 hours = S.
Simplifying the equation gives us: 36 miles/hour = S.
So, Carol's mother needs to drive at least 36 miles per hour to catch up to Carol in 3 hours.
Since the options provided are 35 mph, 39 mph, and 40 mph, the correct answer would be a) 35 mph.