Question

Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks.
Two kids at a summer camp, Franklin and Brenna, are competing in a potato sack race.
Franklin is younger, so he is given a head start of 26 yards. When the race starts, Franklin
hops at a rate of 1 yard per second, and Brenna hops 2 yards per second. Eventually, Brenna
will overtake Franklin. How long will that take? How far will Brenna have to hop?
It will take
seconds for Brenna to hop
yards and catch up to Franklin.

Answer 1

To solve this problem, we can set up a system of equations and solve using substitution. It will take Brenna 26 seconds to catch up to Franklin, and she will have to hop a distance of 52 yards.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let the time in seconds that Franklin and Brenna race be represented by t, and let the distance that Brenna has to hop be represented by d. Franklin's distance can be represented by d + 26, as he has a head start of 26 yards.

We can set up the following equations:

d + 26 = 1t (Franklin's distance formula)

d = 2t (Brenna's distance formula)

Now, we can solve this system of equations using substitution. We can substitute 2t for d in the first equation:

2t + 26 = t

Simplifying this equation, we get:

t = 26

Therefore, it will take Brenna 26 seconds to catch up to Franklin, and she will have to hop a distance of 52 yards.

Learn more about Solving a system of equations to find time and distance in a race