(GENERAL MATHEMATICS)
RATIONAL INEQUALITY
1. Jeo enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Jeo completes the race in less than 2¹/₂ hours, what can we say about his average speeds? What do you call the race that combine three types of event (cycling,swimming, and marathon)? In this time of pandemic, why is it important to keep your body fit and healthy?
2. Sam and Alex play in the same soccer team. Last saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?
Share
Answer:
PROBLEM
Joe enters a race where he has to cycle and run.He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed.Joe completes the race in less than 2½ hours, what can we say about his average speeds?
Answer:
Assign Letters↓
1. Average running speed: s
2. So average cycling speed: 2s
Formulas↓
Speed =
Which can be rearranged to:
Time =
The race is divided into two parts↓
→ CYCLING
Distance = 25 km
Average speed = 2s km/h
So Time = =
→RUNNING
Distance = 20 km
Average speed = s km/h
So Time = =
So Joe completes the race in less than 2½ hours
Then the total time is < 2½
Solution to get the total time is below ↓
252s + 20s < 2½
Solve:
First → 252s + 20s < 2½
Then Multiply all terms by 2s↓
→ 25 + 40 < 5s
Then Simplify → 65 < 5s
Divide both sides by 5 → 13 < s
Swap sides so it's equal to → s > 13
So we already know that Joe average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h.