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 = [tex] \large\frac{Distance}{Time} [/tex]
Which can be rearranged to:
Time = [tex]\large \frac{Distance}{Speed} [/tex]
The race is divided into two parts↓
→ CYCLING
Distance = 25 km
Average speed = 2s km/h
So Time = [tex]\frac{Distance}{Average\:Speed}[/tex]= [tex]\frac{25}{2s}hours[/tex]
→RUNNING
Distance = 20 km
Average speed = s km/h
So Time = [tex]\frac{Distance}{Average\:Speed}[/tex] = [tex]\frac{20}{s} hours[/tex]
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.
#CarryOnLearning
