"Distance" word problems, often also called "uniform rate" problems, involve something travelling at some fixed and steady ("uniform") pace ("rate" or "speed"), or else moving at some average speed. Whenever you read a problem that involves "how fast", "how far", or "for how long", you should think of the distance equation, d = rt, where d stands for distance, r stands for the (constant or average) rate of speed, and t stands for time. Warning: Make sure that the units for time and distance agree with the units for the rate. For instance, if they give you a rate of feet per second, then your time must be in seconds and your distance must be in feet. Sometimes they try to trick you by using the wrong units, and you have to catch this and convert to the correct units.
- A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
- First I'll set up a grid: Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
- d r t first part d 105 t second part 555 – d 115 5 – t total 555 --- 5
- 555 – d = 115(5 – t)
- 555 = 105t + 115(5 – t)
- 555 = 105t + 575 – 115t555 = 575 – 10t–20 = –10t2 = t