Suzette ran and biked for a total of 110 mi in 7 h. Her average running speed was 5 mph and her average biking speed was 20 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Suzette run? 1.5 hours of running
(b) How many hours did she bike? 2 hours of biking
x + y = 7 rearrange as y = 7 - x (1)
And using
Rate * Time = Distance we have that
5 * (x) + 20 (y) = 110 (2)
Sub (1) into (2) for y and we have that
5 * (x) + 20 ( 7 - x) = 110 simplify
5x + 140 - 20x = 110
-15x + 140 = 110 subtract 140 from both sides
-15x = - 30 divide both sides by - 15
x = 2 hours running
And 7 - x = 7 - 2 = 5 hours biking