SOLUTION: Hello, I am having trouble getting started on an equation: a two day marathon walk. total distance of the marathon is 26.2 miles. On the first day, Martha starts walking at 10

Question 502209: Hello,
I am having trouble getting started on an equation:
a two day marathon walk. total distance of the marathon is 26.2 miles. On the first day, Martha starts walking at 10:00am. she walks 4 miles per hour. Carol stars two hours later than Marhta but decides to run to catch up to Martha. Carol runs at a speed of 6 miles per hour.
a. write an equation to represent the distance Martha travels.
b. write and equation to represent the distance Carol travels.
c. solve the system of equations to find when Carol will catch up to Martha.
d. Carol wants to reduce the time she takes to catch up to Martha by 1 hour. How can she do this by changing her starting time? How can she do this by changing her speed?
I am so confused on how to find a starting point to solve this problem. Can you help me write a systems of equations please? Thank you so much EG>

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d = r*t is the basic distance equation.
.
M = Martha's distance.
M = 4 * t
.
C = Carol's distance
C = 6 * t
.
However, their times are different by 2 hr.
If M's time = t, then C's time = t-2.
.
When C catches up, the two have gone the same distance.
M = C
.
4*t = 6*(t-2)
4t = 6t -12
-2t = -12
t = 6
.
So Carol catches up at the 24 mile post.
That would be 4 pm
Carol ran for 4 hours at 6 mph.
Martha walked for 6 hr at 4 mph
.
Carol can catch up an earlier by leaving earlier or by running faster.
Leaving earlier is likely easier.
.
Done.
RELATED QUESTIONS
A local hospital is holding a two day marathon walk to raise funds for a new research... (answered by mananth)

In order to test whether marathon races are bad for health, a researcher took a random... (answered by stanbon)

Out of 260 racers who started the marathon, 228 completed the race, 26 gave up, and 6... (answered by ikleyn,MathTherapy)

Susan ran a marathon. It took her 2 hours to finish the marathon and cover a distance of... (answered by ikleyn)

Hello, I am having trouble trying to figure out how to solve an equation. I just started (answered by josmiceli)

This is pretty confusing how would I do this Of the 20,118 runners who started the... (answered by checkley77)

It takes runners on average 289 minutes to run the marathon. The standard deviation of... (answered by Theo)

It takes runners on average 289 minutes to run the marathon. Drink ZXZ manufacturer... (answered by Theo)

Mateo finished a 21- kilometer marathon while Gerald finished a 15- mile marathon, who... (answered by Alan3354)