Let's solve this step-by-step:
Given:
- Distance run initially = 20 km
- Time taken initially = 2 hours
- New distance to run = 32 km
- New speed = double the previous speed
Step 1: Calculate the initial speed
Speed=DistanceTime=20 km2 hours=10 km/h\text{Speed}=\frac{\text{Distance}}{\text{Time}}=\frac{20\text{ km}}{2\text{ hours}}=10\text{ km/h}Speed=TimeDistance=2 hours20 km=10 km/h
Step 2: Calculate the new speed
New speed=2×10 km/h=20 km/h\text{New speed}=2\times 10\text{ km/h}=20\text{ km/h}New speed=2×10 km/h=20 km/h
Step 3: Calculate the time to run 32 km at the new speed
Time=DistanceSpeed=32 km20 km/h=1.6 hours\text{Time}=\frac{\text{Distance}}{\text{Speed}}=\frac{32\text{ km}}{20\text{ km/h}}=1.6\text{ hours}Time=SpeedDistance=20 km/h32 km=1.6 hours
Final answer:
The boy will take 1.6 hours (or 1 hour and 36 minutes) to run 32 km at double the previous speed.
