# 3 Uniformed Motion Question

Question

Peggy competes in a biathlon by running and bicycling around a large loop through a city. She runs the loop one time and bicycles the loop five times. She can run 8 mph and she can ride 16 mph. If the total time it takes her to complete the race is 1 hr 45 min, determine the distance of the loop.

Answer 1

8r+16b = d +5d = 6d

r+b= 1 hr 45 min = 7/4 hours

r= 7/4 -b

8(7/4-b)+ 16b =6 d

14-8b+16b= 6d

8b = 6d-14

b = 3d/4 - 7/4 = 5d/16

12d -28=5d

7d = 28

d= 28/7 = 4 miles = the loop distance

r = 7/4 -3d/4 +7/4 = 7/2 - 3d/4 = d/8

28 -6d = d

7d =28

d=4 miles

4 miles at 8 mph = 1/2 hour running

4 x 5 =20 miles at 16 mph = 20/16 = 5/4 hour biking 5 loops

1/2 +5/4 = 7/4 hr = 1 hr 45 min