# Mathematical Modelling - Lower Secondary

Mathematical Modelling is part of our Thinking Mathematically collection.

### Where to Land

##### Stage: 4 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

### Slippage

##### Stage: 4 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

### Friday 13th

##### Stage: 3 Challenge Level:

This month there is a Friday the thirteenth and this year there are three. Can you explain why every year must contain at least one Friday the thirteenth?

### Christmas Trees

##### Stage: 3 Challenge Level:

Christmas trees are planted in a rectangular array of 10 rows and 12 columns. The farmer chooses the shortest tree in each of the columns... the tallest tree from each of the rows ... Which is the taller tree, A or B?

### Hands Together

##### Stage: 3 Challenge Level:

Sometime during every hour the minute hand lies directly above the hour hand. At what time between 4 and 5 o'clock does this happen?

### To Run or Not to Run?

##### Stage: 3 Short Challenge Level:

Weekly Problem 38 - 2012
If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

### Martha's Family Tree

##### Stage: 2 and 3 Short Challenge Level:

Weekly Problem 19 - 2013
Can you work out how many descendants Martha has?

### Siblings

##### Stage: 2 and 3 Short Challenge Level:

Weekly Problem 17 - 2013
Anna has 3 brothers and 5 sisters. What is the product of the number of brothers and number of sisters that her brother Tom has?

### Honey Bees

##### Stage: 3 Short Challenge Level:

Weekly Problem 25 - 2007
One gallon of honey provides fuel for one bee to fly about 7,000,000 miles. Roughly how many bees could fly 1000 miles if they had 10 gallons of honey?

### Hiking the Hill

##### Stage: 3 Short Challenge Level:

Weekly Problem 22 - 2011
Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?

### Packing Boxes

##### Stage: 3 Short Challenge Level:

Weekly Problem 28 - 2011
Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

### London Eye

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 18 - 2014
The 80 spokes of the giant wheel The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

### Relative Time

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 25 - 2014
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

### Trolley Park

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 14 - 2016
In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

### Travelling by Train

##### Stage: 3 Short Challenge Level:

Weekly Problem 27 - 2016
Stephen leaves Middlesborough by train at 09:00. The train travels the first 27km at 96km/h. It then stops at Darlington for 3 minutes, before travelling the remaining 29km to Durham at 96km/h. At what time does Stephen arrive at Durham?

### Travelator

##### Stage: 3 Short Challenge Level:

Weekly Problem 25 - 2017
At the airport, the walkway moves with a speed of 4km/h and is 500m long. If Andrew walks with a speed of 6km/h and Bill stands still, how much ahead of Bill is Andrew when he finishes?

### Tennis Training

##### Stage: 3 Short Challenge Level:

Weekly Problem 40 - 2017
After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

### Mathematical Modelling - Short Problems

##### Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Mathematical Modelling.