I need to find how many miles John is in front of Kyle if every two seconds they would complete a turn

Question

They both agreed to match their peddling this meant they would each move their peddles up and down the same number of tones or at the same rate they would complete a turn every 2 seconds the tires on John's bicycle had an 26 inch diameter and kyle's bicylce had an 18 inch diameter tire after one hour how many miles was John in front of Kyle.

Answer 1

circumference=pi*diameter

one hour=3600 seconds

they complete a turn every 2 seconds

3600/2=1800 turns each

John's bike has a circumference of C=pi*d, C=3.14159*26=81.68134 inches

1800*81.68134=147,026.4 inches traveled

147,026.4/12=12,252.16 feet traveled

12,252.16/5280=2.32048 miles traveled

Kyle's bike has a circumference of 3.14159*18=56.5486 inches

1800*56.5486=101,787.4 inches traveled

101,787.4/12=8482.28 feet traveled

8482.28/5280=1.60649 miles traveled

2.32048-1.60649=0.7139 miles ahead

Answer 2

Circumference = π*diameter

The difference in circumference of the tire is the difference in distance traveled every 2 seconds (π*26-π*18).

Every minute 2 seconds passes 30 times (60/2).

Every hour 60 minutes pass.

So 2 seconds pass 1800 times in an hour (60/2*60).

 

Therefore the difference between John's travel and Kyle's is found as follows:

(π*26-π*18)*1800 = 45238.934 inches

 

There are 63360 inches in one mile, so

45238.934/63360 = .714

 

About .714 miles