Question

Kari leaves the school traveling 30 mph for h hours. After Kari has driven for 10 miles, Patty leaves the school traveling 35 mph for h hours. After how many hours will Kari and Patty have driven the same amount of miles?

A) 2 hours
B) 1 hour
C) 1.5 hours
D) 3 hours

Answer 1

Kari and Patty will have driven the same number of miles after 2 hours, which is found by equating the distances they travel and solving for the time 'h'. The correct answer option is A) 2 hours.

Step-by-step explanation:

To determine when Kari and Patty have driven the same number of miles, we need to set up an equation based on the distances they each travel and solve for h, the number of hours at which their total distances are equal. We know Kari drives for h hours at a speed of 30 mph and Patty drives for h hours at a speed of 35 mph, but starts 10 miles later.

Kari's distance is equal to 30 mph multiplied by h hours. Patty's distance is 35 mph multiplied by h minus the 10 miles head start Kari had. Setting these two distances equal to each other gives us the equation:

30h = 35h - 10

By solving this equation for h, we subtract 30h from both sides:

0 = 5h - 10

Then, we add 10 to both sides to isolate 5h:

10 = 5h

Finally, we divide both sides by 5 to solve for h:

h = 2 hours

So, after 2 hours, Kari and Patty will have driven the same amount of miles. The correct answer is option A) 2 hours.