Question

Charles City has built 5 km of bicycle paths by the end of the first month, and the total length of the paths doubles each month. Tinsel Town has built 21 km of bicycle paths by the end of the first month, and the total length of the paths increases by 5 km per month. At the end of which month does the total length of the bicycle paths in Charles City first exceed the length in Tinsel Town?

a. 2nd month

b. 3rd month

c. 4th month

d. 5th month

Answer 1

The total length of bicycle paths in Charles City will first exceed the length in Tinsel Town at the end of the 4th month, with Charles City having 40 km and Tinsel Town 36 km.

Step-by-step explanation:

To determine when the length of bicycle paths in Charles City will exceed Tinsel Town, we need to calculate the total length for each city over the course of several months. Charles City starts with 5 km of paths and doubles this amount each month, while Tinsel Town starts with 21 km and adds 5 km each month.

• End of 1st month: Charles City = 5 km, Tinsel Town = 21 km
• End of 2nd month: Charles City = 5 km × 2 = 10 km, Tinsel Town = 21 km + 5 km = 26 km
• End of 3rd month: Charles City = 10 km × 2 = 20 km, Tinsel Town = 26 km + 5 km = 31 km
• End of 4th month: Charles City = 20 km × 2 = 40 km, Tinsel Town = 31 km + 5 km = 36 km

At the end of the 4th month, the total length of the bicycle paths in Charles City (40 km) will exceed the length in Tinsel Town (36 km). Therefore, the correct answer is c. 4th month.