the total distance covered by one person or vehicle; and the total time it took that person or vehicle to cover the distance. For example:[1] X Research source If Ben traveled 150 miles in 3 hours, what was his average speed?
For example, if Ben drives 150 total miles, your formula will look like this: S=150t{\displaystyle S={\frac {150}{t}}}.
For example, if Ben drives for 3 hours, your formula will look like this: S=1503{\displaystyle S={\frac {150}{3}}}.
For example:S=1503{\displaystyle S={\frac {150}{3}}}S=50{\displaystyle S=50}So, if Ben traveled 150 miles in 3 hours, his average speed is 50 miles per hour.
multiple distances that were traveled; and the amount of time it took to travel each of those distances. [3] X Research source For example: If Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in 1 hour, what was his average speed for the entire trip?
For example, If Ben traveled 150 miles, 120 miles, and 70 miles, you would determine the total speed by adding the three distances together: 150+120+70=340{\displaystyle 150+120+70=340}. So, your formula will look like this: S=340t{\displaystyle S={\frac {340}{t}}}.
For example, If Ben for 3 hours, 2 hours, and 1 hour, you would determine the total time by adding the three times together: 3+2+1=6{\displaystyle 3+2+1=6}. So, your formula will look like this: S=3406{\displaystyle S={\frac {340}{6}}}.
For example:S=3406{\displaystyle S={\frac {340}{6}}}S=56. 67{\displaystyle S=56. 67}. So if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in 1 hour, his average speed was about 57 mph.
multiple speeds used to travel; and the amount of time each of those speeds was traveled for. [5] X Research source For example: For example: If Ben traveled 50 mph for 3 hours, 60 mph for 2 hours, and 70 mph for 1 hour, what was his average speed for the entire trip?
For example:50 mph for 3 hours = 50×3=150miles{\displaystyle 50\times 3=150{\text{miles}}}60 mph for 2 hours = 60×2=120miles{\displaystyle 60\times 2=120{\text{miles}}}70 mph for 1 hour = 70×1=70miles{\displaystyle 70\times 1=70{\text{miles}}}So, the total distance is 150+120+70=340miles. {\displaystyle 150+120+70=340{\text{miles}}. } So, your formula will look like this: S=340t{\displaystyle S={\frac {340}{t}}}
For example, If Ben for 3 hours, 2 hours, and 1 hour, you would determine the total time by adding the three times together: 3+2+1=6{\displaystyle 3+2+1=6}. So, your formula will look like this: S=3406{\displaystyle S={\frac {340}{6}}}.
For example:S=3406{\displaystyle S={\frac {340}{6}}}S=56. 67{\displaystyle S=56. 67}. So if Ben traveled 50 mph for 3 hours, 60 mph for 2 hours, and 70 mph for 1 hour, his average speed was about 57 mph.
two or more different speeds; and that those speeds were traveled for the same amount of time. For example, if Ben drives 40 mph for 2 hours, and 60 mph for another 2 hours, what is his average speed for the entire trip?
In these types of problems, It doesn’t matter for how long each speed is driven, as long as each speed is used for half the total duration of time. You can modify the formula if you are given three or more speeds for the same amount of time. For example, s=a+b+c3{\displaystyle s={\frac {a+b+c}{3}}} or s=a+b+c+d4{\displaystyle s={\frac {a+b+c+d}{4}}}. As long as the speeds were used for the same amount of time, your formula can follow this pattern.
For example, if the first speed is 40 mph, and the second speed is 60 mph, your formula will look like this: s=40+602{\displaystyle s={\frac {40+60}{2}}}.
For example:s=40+602{\displaystyle s={\frac {40+60}{2}}}s=1002{\displaystyle s={\frac {100}{2}}}s=50{\displaystyle s=50}So, if Ben traveled 40 mph for 2 hours, then 60 mph for another 2 hours, his average speed is 50 mph.
two different speeds; and that those speeds were used for the same distance. For example, if Ben drives the 160 miles to the waterpark at 40 mph, and returns the 160 miles home driving 60 mph, what is his average speed for the entire trip?
Often problems requiring this method will involve a question about a return trip. In these types of problems, it doesn’t matter how far each speed is driven, as long as each speed is used for half the total distance. You can modify the formula if given three speeds for the same distance. For example, s=3abcab+bc+ca{\displaystyle s={\frac {3abc}{ab+bc+ca}}}. [9] X Research source
For example, if the first speed is 40 mph, and the second speed is 60 mph, your formula will look like this: s=(2)(40)(60)40+60{\displaystyle s={\frac {(2)(40)(60)}{40+60}}}.
For example:s=(2)(40)(60)40+60{\displaystyle s={\frac {(2)(40)(60)}{40+60}}}s=480040+60{\displaystyle s={\frac {4800}{40+60}}}.
For example:s=480040+60{\displaystyle s={\frac {4800}{40+60}}}s=4800100{\displaystyle s={\frac {4800}{100}}}.
For example:s=4800100{\displaystyle s={\frac {4800}{100}}}s=48{\displaystyle s=48}. So, if Ben drives 40 mph for 160 miles to the waterpark, then 60 mph for the 160 miles home, his average speed for the trip is 48 mph.
