Name: Sarah
Who is asking: Student
Question: The first thing I would do to solve this problem is draw a diagram illustrating the information you know. Joe = 6 km/h , Dad = 30 km/h X Joe start dad starts dad catches up time = 0 Joe's time = 4 h time = ? Now ask yourself the question "how far did Joe travel before his dad started?" Using rate x time = distance we can calculate that Joe travelled 6 km/h x 4 h = 24 km before his dad left in the motor boat. This is the distance that his father must "make up" in order to overtake Joe. Now ask yourself the question, "how much faster is the motorboat going than Joe?" Joe goes 6 km/h and his dad goes 30 km/h so dad travels 24 km/h faster than Joe. That means that every hour he travels he will "make up" 24 km. From this we see that Joe's dad will overtake him in one hour. At that time, that is, after 5 hours total, Joe will have travelled a total of 6 km/h x 5 h = 30 km. Here's another way to view it: Joe and his dad will have both traveled the same distance at the time Joe's canoe is overtaken by his dad's motorboat.
Use our distance formula: rate x time = distance together with our known info:
Joe travels a distance = 6 km/h x (4 + t)
Now equate the two distances and solve for t: 24 + 6t = 30t 24 = 24t 1 = t which is the same answer as we came up with previously for the time it takes his father to overtake him.
Hope this helps,
