You begin your trip at 8 a.m., travel at a rate of 60 miles per hour, and reach your destination at 12 p.m. How far have you traveled? To find the total distance traveled, multiply the time traveled by the rate or speed. The formula is distance = rate x...
You begin your trip at 8 a.m., travel at a rate of 60 miles per hour, and reach your destination at 12 p.m. How far have you traveled? To find the total distance traveled, multiply the time traveled by the rate or speed. The formula is distance = rate x time, or D=R*T. So to solve the problem above, we multiply 4 hours (8 a.m. to 12 p.m.) by 60 miles per hour to reach a distance of 240 miles.
Let's try a problem that is a bit more difficult. Let's say you begin your journey at 9 a.m. For the first two hours, you travel at 55 miles per hour. Then you are able to pick up speed on the freeway and travel at 65 miles per hour until 1 p.m. How far have you traveled?
We must solve this question in sections. Let's calculate the distance covered in the first two hours. Multiply 2 hours by 55 miles per hour for a total of 110 miles. Now let's find the distance for the last part of the trip. Since, you've already traveled two hours, it is now 11 a.m. You travel until 1 p.m., so that is two more hours. Now you can go at 65 miles per hour, so we multiple that by 2 hours to get 130 miles. So, adding together 110 and 130, you've covered a total of 240 miles.
Let's try one more, this time a bit more complicated yet. You start your trip at 8:30 a.m. and travel at 40 miles per hour for the first fifteen minutes. Then you speed up to 55 miles per hour and travel for another hour and a half. Finally, you slow back down to 50 miles per hour and reach your destination in another half hour. How far have you traveled?
Again, we'll work in sections, applying the distance = rate x time formula three times. First, you travel for fifteen minutes, or 0.25 of an hour, at 40 miles per hour. Multiple those, and you discover that you have traveled 10 miles. Now you travel at 55 miles per hour for 1.5 hours. Multiple those to get 82.5 miles. Finally, you travel 50 miles per hour for 0.5 hours, covering another 25 miles. Add those three sections of your trip together, and you have traveled 117.5 miles.