Loading…
Example 3.52 from Elementary Algebra, 3.5 Solve Uniform Motion Applications
Solve Uniform Motion Applications: example 3.52
Hamilton loves to travel to Las Vegas, 255 miles from his home in Orange County. On his last trip, he left his house at 2:00 pm. The first part of his trip was on congested city freeways. At 4:00 pm, the traffic cleared and he was able to drive through the desert at a speed 1.75 times faster than when he drove in the congested area. He arrived in Las Vegas at 6:30 pm. How fast was he driving during each part of his trip?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
A diagram will help us model this trip.
Next, we create a table to organize the information.
We know the total distance is 255 miles. We are looking for the rate of speed for each part of the trip. The rate in the desert is 1.75 times the rate in the city. If we let the rate in the city, then the rate in the desert is
The times here are given as clock times. Hamilton started from home at 2:00 pm and entered the desert at 4:30 pm. So he spent two hours driving the congested freeways in the city. Then he drove faster from 4:00 pm until 6:30 pm in the desert. So he drove 2.5 hours in the desert.
Now, we multiply the rates by the times.
By looking at the diagram below, we can see that the sum of the distance driven in the city and the distance driven in the desert is 255 miles.
Translate into an equation. Solve this equation. Check. Hamilton drove 40 mph in the city and 70 mph in the desert.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Cruz is training to compete in a triathlon. He left his house at 6:00 and ran until 7:30. Then he rode his bike until 9:45. He covered a total distance of 51 miles. His speed when biking was 1.6 times his speed when running. Find Cruz’s biking and running speeds.
How did it go?