Answer:
6 miles
Step-by-step explanation:
Let the route length be r. The distance the cyclist has already covered is then (5/7)r + 40. This plus 0.75r - 118 must = r, the length of the entire route.
Then:
(5/7)r + 40 + (3/4)r - 118 = r
The LCD of the fractions 5/7 and 3/4 is 28. We thus have:
(20/28)r + 40 + (21/28)r - 118 = r, or
(41/28)r - 78 = (28/28)r
Combining the r terms, we get 13r = 78, and so r = 78/13 = 6.
The cyclist's bike route is 6 miles long.
