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A person travels from home to Mula Trading Centre by bicycle, then drives to a town and back to Mula, and finally cycles back home. Calculate the total distance and time.

Mathematics

ScanSolve AI Answer

Answer

3

4623 km/h\text{46}\frac{2}{3} \text{ km/h}

Step-by-step solution

3 steps

Step 1: Calculate the distance and time for each part of the journey.

Part 1

Cycling from home to Mula Trading Centre

The distance is given as 30 km.
The time taken is given as 2122\frac{1}{2} hours.

d1=30 kmd_1 = 30 \text{ km} t1=2.5 hourst_1 = 2.5 \text{ hours}

Part 2

Driving from Mula to a town and back to Mula

The distance to the town is 180 km, and he drove back to Mula, so the return distance is also 180 km.
The total distance for this part is:

d2=180 km+180 km=360 kmd_2 = 180 \text{ km} + 180 \text{ km} = 360 \text{ km}

The average speed for this part is 80 km/h.
The time taken for this part is:

t2=DistanceSpeed=360 km80 km/h=4.5 hourst_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{360 \text{ km}}{80 \text{ km/h}} = 4.5 \text{ hours}

Part 3

4623 km/h\text{46}\frac{2}{3} \text{ km/h}

Cycling from Mula back home

Mula Trading Centre is 30 km from his home, so the distance back home is 30 km.

d3=30 kmd_3 = 30 \text{ km}

The average speed for this part is 15 km/h.
The time taken for this part is:

t3=DistanceSpeed=30 km15 km/h=2 hourst_3 = \frac{\text{Distance}}{\text{Speed}} = \frac{30 \text{ km}}{15 \text{ km/h}} = 2 \text{ hours}

  1. Calculate the total distance for the whole journey.

    Dtotal=d1+d2+d3D_{total} = d_1 + d_2 + d_3 Dtotal=30 km+360 km+30 kmD_{total} = 30 \text{ km} + 360 \text{ km} + 30 \text{ km} Dtotal=420 kmD_{total} = 420 \text{ km}

  2. Calculate the total time for the whole journey.

    Ttotal=t1+t2+t3T_{total} = t_1 + t_2 + t_3 Ttotal=2.5 hours+4.5 hours+2 hoursT_{total} = 2.5 \text{ hours} + 4.5 \text{ hours} + 2 \text{ hours} Ttotal=9 hoursT_{total} = 9 \text{ hours}

  3. Calculate the average speed for the whole journey.

    The average speed is the total distance divided by the total time.

    Average Speed=DtotalTtotal\text{Average Speed} = \frac{D_{total}}{T_{total}} Average Speed=420 km9 hours\text{Average Speed} = \frac{420 \text{ km}}{9 \text{ hours}} Average Speed=1403 km/h\text{Average Speed} = \frac{140}{3} \text{ km/h} Average Speed≈46.67 km/h\text{Average Speed} \approx 46.67 \text{ km/h}

    The average speed for the whole journey is:

    4623 km/h\boxed{\text{46}\frac{2}{3} \text{ km/h}}
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