Is this the correct answer to the following question?
"You can ride a bicycle 15 mph. Your sister rides 12 mph. You give her a one hour head start. In how many hours will you catch up if neither of you stops?"
15-12= 3
12/3= 4
My answer: 4 hours.
The relative velocity is 3mph. When she starts, she is 12mi ahead.
It takes 4 hours to close that distance. If I gave my sister that much of a lead, I would just let her go alone.
Is my answer correct, then?
yes.
To solve this problem correctly, we need to consider the relative speeds and the head start given to your sister. Let's break it down step by step:
1. Determine the relative speed: Your speed is 15 mph, while your sister's speed is 12 mph. To find the relative speed, subtract your sister's speed from your speed: 15 - 12 = 3 mph.
2. Calculate the time it takes to catch up: Since you gave your sister a one-hour head start, you need to find the time it takes for you to cover the distance between you and your sister at your relative speed of 3 mph.
To do this, divide the distance by the relative speed:
1 hour (head start) * 3 mph (relative speed) = 3 miles.
3. Calculate the catching up time: To determine the time it takes for you to catch up to your sister, divide the distance you need to cover (3 miles) by your speed (15 mph):
3 miles / 15 mph = 0.2 hours.
So, the correct answer is 0.2 hours, which is equivalent to 12 minutes. It will take you approximately 12 minutes to catch up to your sister if neither of you stops.