1. Distance & Motion Problems d=rt formula distance chart Copyright © 2013 by Lynda Aguirre1

2. Distance Formula Copyright © 2013 by Lynda Aguirre2 d = r t distance = rate x time (how far) = (how fast, speed) x (how long it takes) Section A: One object traveling in one direction

3. Copyright © 2013 by Lynda Aguirre3 Section A: One object traveling in one direction Distance Formula a. A bird flies at a speed of 8 mph for 2 hours. How far did the bird travel? One object moving: Distance Formula: d = r t (distance = rate x time) d = (8)(2) d= 16 miles What information is given? Speed (this is the rate), r = 8 mph Travel time, t = 2 hours Distance? = unknown (How far means we don’t know the distance)

4. Copyright © 2013 by Lynda Aguirre4 Section A: One object traveling in one direction Distance Formula b. If a bird flies at a speed of 10 mph, how long would it take for the bird to travel a distance of 30 miles? One object moving: Distance Formula: d = r t (distance = rate x time) 30 = (10)t t = 3 hours What information is given? Speed (this is the rate), r = 10 mph Travel time, (how long=unknown time) Distance, d=30 miles

5. Copyright © 2013 by Lynda Aguirre5 Section A: One object traveling in one direction Distance Formula c. If a bird flies 17 miles in 3 hours, what was its speed? One object moving: Distance Formula: d = r t (distance = rate x time) 17 = r(3) r = 5.7 mph What information is given? Speed, r = unknownTravel time, t=3 hours Distance, d=17 miles 17 = 3r Round off to one decimal place r = 5.66… Rearrange: Number comes first

6. Copyright © 2013 by Lynda Aguirre6 Time Conversion Problems When calculating distance problems, you will often run into a situation where the time has to be converted from decimal form into the more commonly used hour/minute format. The next example demonstrates this process

7. Copyright © 2013 by Lynda Aguirre7 Section A: One object traveling in one direction Distance Formula b. If a bird flies at a speed of 10 mph, how long would it take for the bird to travel a distance of 12 miles? One object moving: Distance Formula: d = r t (distance = rate x time) 12 = (10)t t = 1.2 hours What information is given? Speed (this is the rate), r = 10 mph Travel time, (how long=unknown time) Distance, d=12 miles Convert to hours and minutes

8. Copyright © 2013 by Lynda Aguirre8 t = 1.2 hours Time Conversion Problems Time conversion: 60 minutes in an hour.2 x 60 = 12 minutes The hours are given by the number to the left of the decimal The minutes must be changed from.2 hours into minutes t = 1 hour 12 minutes

9. Copyright © 2013 by Lynda Aguirre9 Practice Problems 1) A bird flies 18 miles in 3 hours. How fast was the bird traveling? 2) A bird flies at a speed of 8 miles per hour for 6 hours. How far did the bird travel? 3) A bird flies 25 miles in 5 hours. How fast was the bird flying? 4) A bird flies at a speed of 6 miles per hour and travels 37 miles. How long did the trip take? Use the distance formula to solve the following problems. Convert your answers into standard units when necessary.