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.