Jill was training for a triathlon, so she planned a day of exercising. She spent a total of 2 hours riding her bike and running. She biked for 12 miles and ran for 6 miles. Her rate for running was 10 mph less than her biking rate. What was her rate when running?

Jill's rate of running = 4.667 miles/hr

Step-by-step explanation:

Let's say that rate of running = x miles/hr

so rate of biking = (x + 10) miles / hr

Time of running = rate of running / distance of running = x/6

Time of biking = rate of biking/distance of biking = (x+10) / 12

Total time of cycling and biking = Time of running + Time of biking

Given that total time of cycling and biking = 2 hrs

⇒ 2 = (x/6) + ((x+10) / 12)

⇒ 2 = (2x+x + 10) / 12

⇒ 2 * 12 = 3x + 10

⇒24 - 10 = 3x

⇒x = 14/3 = 4.667 miles/hr

Hence Jill's rate of running = 4.667 miles/hr