Starting at home, Luis travelled uphill to the toy store for 12 min at 15 mph. He then travels back home along the same path, downhill at a speed of 30mph. What is his average speed for the entire trip, up and back from the toy store.
I know that the amount of time downhill is 6 minutes, but I can't understand how to find the speed. There is a multiplication formula used in the final equation, and I just don't understand why the multiplication is used.
Speed is always measured as distance over time, so for example, if you are travelling in a car and you drive 60 miles in one hour, you are travelling 60 mph which is really 60 Miles / 1 Hour.
It's an actual example of when it's OK to compare "apples and oranges", dividing one concept by a different, related one
So, to find the distance, 12 minutes at 15 miles / 60 minutes, we first find the value of 12/60 (What portion of the hour did he drive) which is 1/5.
Then we multiply 1/5 * 15 miles = 3 Miles. If you are travelling 15mph, you will travel 3 Miles in 12 minutes.
Now if we want to find the time it takes to get home at 30mph, we divide the 30 miles you would travel in one hour, by the 3 miles actually travelled (What portion of the miles did he drive), to get 1/10.
Then we multiply 1/10 * 60 Minutes = 6 Minutes. If you are travelling 30mph, you will travel 3 Miles in 6 minutes.
Now to find the average speed we need to account for each leg of the journey based on it's distance, so:
3 miles * 15mph = 45. 3 miles * 30mph = 90. Now we add the two together: 45 + 90 = 135.
Lastly we divide that total 135 by the total number of miles traveled, 6. 135/6 = 22.5 mph is the average speed.
This is because we need to average the speed for the entire trip, and although in this case both legs were the same distance, and you could have just averaged 15 and 30 to get 22.5, it's important to remember how to do it if each leg were a different distance..
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