QUESTIONS

1.

Don competes in a biathlon race. The race has two sections: A swim across a lake A cycle around the lake

The distances covered and times taken for each section are:

Calculate Don’s average speed in kilometres per hour for the swim section.

Calculate Don’s average speed for the entire race.

Section Distance Time

Swim 600 m 15 minutes

Cycle 20 km 45 minutes

2 a.

When she walks to school from home, Jenny walks 260 m from her house to the main road, then half a kilometre along the main road and finally 120 m from the main road to the school gate.

State each part of the journey as a distance in kilometres.

Calculate the total distance Jenny has walked in metres and in kilometres.

2 b.

Jenny hurries from her house because she is going to meet her friend Heta. Jenny takes 3 minutes (0.05 hours) to reach the main street. Jenny and Heta dawdle along the main road, taking 12 minutes (0.2 hours) to reach the turn-off to school. When they get there, they realise they are late, so they run to the school gate at a constant speed of 8 km h-1. Calculate Jenny’s average speed (in kilometres per hour)

during the first part of her journey. Calculate Jenny’s average speed (in kilometres per hour) from

home to the turn-off from the main road. Calculate the time (in seconds) it takes Jenny and Heta to run

to the school gate. Jenny’s brother, Jim, cycles the same route to school in 10

minutes. In terms of distance and time, explain how you know that Jim cycles faster than Jenny walks.

3.

Section of

journey

Distanc

e

Time (h) Speed

Wellington

to Taupo

380 km 5 hours  

Lunch   1 hour  

Taupo to

Waitomo

220 km    

Coffee   ½ hour  

Waitomo to

Auckland

  2 ½ hours 80 km h-1

Whole

journey

  12 hours  

3.b

Calculate the average speed from Wellington to Taupo.

Calculate how long it would take to travel from Taupo to Waitomo if they average the same speed as in the first leg of their journey from Wellington to Taupo.

Calculate their actual average speed from Taupo to Waitomo.

3.C

Calculate the distance they travelled from Waitomo to Auckland.

Calculate the average speed for the whole journey.

Explain why the average speed for the whole journey is less than the speeds they were averaging in each section of the journey.