Laura Hoye drives along an interstate highway at 70 mph until she encounters heavy traffic and has to slow to 50 mph.

Question

The time she drove at 70 mph is 1 hour more than the time she drove at 50 mph and the distance she drove at 70 mph is greater than the distance she drove at 50 mph. If the difference in the distance she drove at 70 mph and the distance she drove at 50 mph is 100 miles, determine the time she spent at each speed.

Answer 1

distance = rate x time

 

x = 70(t + 1)

x - 100 = 50t

 

70(t+1) - 100 = 50t

 

70t -30 = 50t

20t = 30

t = 1.5 hours at 50 mph

t+1 = 2.5 hours at 70 mph

 

distance traveled at 50mph = 50 x 1.5 = 75 miles

distance traveled at 70mph = 70 x 2.5 = 175

 

175 - 75 = 100  CORRECT