MATHHHHHHHHHH

Question

As part of her training routine for basketball, ali alternates between cycling and running for exercise. She cycles at a rate of 12mph and runs at a rate of 6mph. If she spends 7.5 hours exercising and covers a total of 78 miles, how much time did she spend on each exercise

Answer 1

distance cycling = 12t where t=hours cyclling

distance running = 6(7.5-t)  or  45 -6t, after distributing.

 

Total distance = 78 = 12t + 45 - 6t.  Get it? 

 

Solve for t to get answer (# hrs cycling) and then also # hrs running.

Answer 2

78 miles = distance running + distance cycling

 

 78 miles = 6 * time running + 12 * time cycling  <---- label this equation ALPHA

 

 

time running + time cycling = 7.5

 

time running = 7.5 - time cycling <--- label this equation BETA

 

Substituting BETA into ALPHA

 

78 = 6 ( 7.5 - time cycling) + 12 * time cycling

 

78 = 45 - 6 * time cycling + 12 * time cycling

 

78 = 45 + 6 * time cycling

 

33 = 6 * time cycling

 

33/6 = time cycling

 

11/2 = time cycling

 

time running = 7.5 - 11/2 = 7.5 - 5.5 = 2

 

2 * 6 + 12 * 5.5 = 12 + 66 = 78

 

He spends 2 hours running

and 5.5 hours cycling.