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.

Question

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.

Answer 1

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

Answer 2

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

Answer 3

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