A person walks 30 km towards north and walked 40km east how far is he from the starting point
Chapter 8: Rational Expressions 8.8 Rate Word Problems: Speed, Distance and TimeDistance, rate and time problems are a standard application of linear equations. When solving these problems, use the relationship rate (speed or velocity) times time equals distance.
For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h)(4h) = 120 km. The problems to be solved here will have a few more steps than described above. So to keep the information in the problem organized, use a table. An example of the basic structure of the table is below: Example of a Distance, Rate and Time Chart
The third column, distance, will always be filled in by multiplying the rate and time columns together. If given a total distance of both persons or trips, put this information in the distance column. Now use this table to set up and solve the following examples. Joey and Natasha start from the same point and walk in opposite directions. Joey walks 2 km/h faster than Natasha. After 3 hours, they are 30 kilometres apart. How fast did each walk?
The distance travelled by both is 30 km. Therefore, the equation to be solved is: This means that Natasha walks at 4 km/h and Joey walks at 6 km/h. Nick and Chloe left their campsite by canoe and paddled downstream at an average speed of 12 km/h. They turned around and paddled back upstream at an average rate of 4 km/h. The total trip took 1 hour. After how much time did the campers turn around downstream?
The distance travelled downstream is the same distance that they travelled upstream. Therefore, the equation to be solved is: This means the campers paddled downstream for 0.25 h and spent 0.75 h paddling back. Terry leaves his house riding a bike at 20 km/h. Sally leaves 6 h later on a scooter to catch up with him travelling at 80 km/h. How long will it take her to catch up with him?
The distance travelled by both is the same. Therefore, the equation to be solved is: This means that Terry travels for 8 h and Sally only needs 2 h to catch up to him. On a 130-kilometre trip, a car travelled at an average speed of 55 km/h and then reduced its speed to 40 km/h for the remainder of the trip. The trip took 2.5 h. For how long did the car travel 40 km/h?
The distance travelled by both is 30 km. Therefore, the equation to be solved is: This means that the time spent travelling at 40 km/h was 0.5 h. Distance, time and rate problems have a few variations that mix the unknowns between distance, rate and time. They generally involve solving a problem that uses the combined distance travelled to equal some distance or a problem in which the distances travelled by both parties is the same. These distance, rate and time problems will be revisited later on in this textbook where quadratic solutions are required to solve them. QuestionsFor Questions 1 to 8, find the equations needed to solve the problems. Do not solve.
Solve Questions 9 to 22.
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