The most important equation to remember for distance problems is:

(Speed)*(Time)= Distance

Usually, however, questions will not be presented to you so simply and you will have to manipulate this equation to find your answer.

Take, for instance, this example:

Train 1 leaves Kaohsiung at 12pm and heads directly to Taipei. It travels at a speed of 90 miles an hour and makes no stops. Train 2 leaves Taipei 2 hours later, and heads directly to Kaohsiung, making no stops. Kaohsiung and Taipei are 360 miles apart. If the trains pass each other at 3pm, how fast is train 2 going?

- 70 mph
- 85 mph
- 90 mph
- 95 mph
- 100 mph

Unfortunately, this problem isn’t as simple as plugging in speed and time to get distance. It’s not even as simple as plugging in distance and time to get speed. You have to use the information you have and manipulate the equations to get the speed. This is how:

We know the total distance both trains together have traveled when they pass each other is 360 miles. This is because they will pass each other at some point in between Taipei and Kaohsiung, one will have traveled part of the difference and the other will have traveled the rest.

We also know the total distance that train 1 will have traveled when they pass each other, because we know its sped (90 miles per hour) and how long it has been traveling (3 hours), because it leaves at noon and they pass each other at 3. So train 1’s distance is

(90 miles/hour)(3 hours)= 270 miles

We can then use that information to figure out train 2’s distance, because

T1distance+T2distance= 360 miles

Therefore Train 2’s distance is 90 miles. It travels this distance in one hour, because it leaves at 2 (2 hours after Train 1) and they pass at 3. Therefore, is speed is:

(Speed)(1hour)=9 miles therefore, speed= 90 miles per hour.

Like other question types, speed and distance questions need to be broken down into their key elements and then the basic equations can be manipulated to figure out the answer.

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