Abicyclist covered 5/7 of his route and an additional 40 miles. he has yet to cover 118 miles less than 0.75 of his route. how long is his route in miles?

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.

step-by-step explanation: