Are there any traveling circus left?

Naomi left the cafe traveling 12 mph. Then, 4 hours later, Amy left traveling the same direction at 28 mph..?

• Naomi left the cafe traveling 12 mph. Then, 4 hours later, Amy left traveling the same direction at 28 mph. How long until Amy catches up with Naomi?

• Answer:

  After 4 hours, Naomi has gone 48mph. That's her head start. For every hour after, she goes another 12 miles. For every hour after, Amy goes 28mph. Let x be the number of hours until Amy catches up. So after x hours, Naomi has gone 48 + 12x miles, and Amy has gone 28x miles. For what value of x are their distances equal? 48 + 12x = 28x Subtract 12x from both sides. 48 = 16x 3 = x That's the math way! The logical way is even shorter to solve: Once Amy starts traveling, she will catch up to Naomi 16 miles every hour (she's going 28, Naomi is only going 12). So, at 16mph catch-up per hour, it will take her 3 hours to wipe out the 48 mile head start.