On a reality TV show, contestants have to perform tasks on an island. They are given the map of the island shown below. Two points, A and B, are marked with X's. Basecamp is also marked. The contestants are told that treasure is buried on the island at a point T. T is 20 km from A and 20 km from B. (i) The map is drawn to a scale of 1 cm to 5 km. On the map, how far is T from the point A? (ii) Using a compass, construct the point T on the map. Label the point T. (iii) Measure the distance from the point T to Basecamp on your map, and hence find the actual distance, in km, from the point T to Basecamp. (iv) The contestants find the treasure at 13:00 and return to Basecamp immediately. If they walk at an average speed of 6 km per hour, find the time they reach Basecamp immediately. Question 8 (Suggested maximum time: 10 minutes) Olive cycled to the shop to get some milk for her tea. She cycled along a particular route and returned by the same route. The graph below shows the different stages of her journey. (i) How long did Olive stay in the shop? (ii) How far from her home is the shop? (iii) Compare the speed of her trip to the shop with her speed on the way home. (iv) Write a paragraph to describe her journey.

Junior Cycle Mathematics Distance, Speed and Time: On a reality TV show, contestant

On a reality TV show, contestants have to perform tasks on an island - Junior Cycle Mathematics - Question 8 - 2014

Question 8

On a reality TV show, contestants have to perform tasks on an island. They are given the map of the island shown below. Two points, A and B, are marked with X's. Bas... show full transcript

Worked Solution & Example Answer:On a reality TV show, contestants have to perform tasks on an island - Junior Cycle Mathematics - Question 8 - 2014

Step 1

i) The map is drawn to a scale of 1 cm to 5 km. On the map, how far is T from the point A?

96%

114 rated

Answer

To find the distance from A to T on the map, we first convert the actual distance into the map's scale. Since T is 20 km from A and the scale is 1 cm to 5 km, we divide 20 km by 5 km/cm:

ext{Distance on map} = \frac{20 \text{ km}}{5 \text{ km/cm}} = 4 \text{ cm}

Thus, T is 4 cm from point A on the map.

Step 2

ii) Using a compass, construct the point T on the map. Label the point T.

99%

104 rated

Answer

Using a compass, locate 4 cm from point A towards the direction indicated for T, then mark this point and label it T.

Step 3

iii) Measure the distance from the point T to Basecamp on your map, and hence find the actual distance, in km, from the point T to Basecamp.

96%

101 rated

Answer

After measuring on the map, let's assume the distance from T to Basecamp is found to be 3.5 cm. Given the scale, we calculate the actual distance:

ext{Actual distance} = 3.5 \text{ cm} \times 5 \text{ km/cm} = 17.5 \text{ km}

Step 4

iv) The contestants find the treasure at 13:00 and return to Basecamp immediately. If they walk at an average speed of 6 km per hour, find the time they reach Basecamp immediately.

98%

120 rated

Answer

To find the time taken to travel back to Basecamp:

ext{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{17.5 \text{ km}}{6 \text{ km/h}} = 2.9167 \text{ hours} \approx 2 \text{ hours and } 55 \text{ minutes}

They return at approximately 15:55.

Step 5

i) How long did Olive stay in the shop?

97%

117 rated

Answer

Olive stayed in the shop from the 20th minute until the 35th minute. This indicates she was in the shop for:

35 - 20 = 15 \text{ minutes}

Step 6

ii) How far from her home is the shop?

97%

121 rated

Answer

The graph indicates that the first leg of her journey to the shop extended for a distance of 5 km. Therefore, the shop is 5 km away from her home.

Step 7

iii) Compare the speed of her trip to the shop with her speed on the way home.

96%

114 rated

Answer

Olive's trip to the shop took 20 minutes, while the return took 10 minutes. Therefore:

The speed to the shop is calculated as:

\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5 \text{ km}}{1/3 \text{ hour}} = 15 \text{ km/h}

The speed on the way home is:

\text{Speed} = \frac{5 \text{ km}}{1/6 \text{ hour}} = 30 \text{ km/h}

Hence, Olive cycled faster on the way home.

Step 8

iv) Write a paragraph to describe her journey.

99%

104 rated

Answer

Olive took 20 minutes to cycle 5 km to the shop. She stayed there for 15 minutes and then cycled back home in 10 minutes. Thus, her total trip took 20 + 15 + 10 = 45 minutes.

On a reality TV show, contestants have to perform tasks on an island - Junior Cycle Mathematics - Question 8 - 2014

Worked Solution & Example Answer:On a reality TV show, contestants have to perform tasks on an island - Junior Cycle Mathematics - Question 8 - 2014

i) The map is drawn to a scale of 1 cm to 5 km. On the map, how far is T from the point A?

ii) Using a compass, construct the point T on the map. Label the point T.

iii) Measure the distance from the point T to Basecamp on your map, and hence find the actual distance, in km, from the point T to Basecamp.

iv) The contestants find the treasure at 13:00 and return to Basecamp immediately. If they walk at an average speed of 6 km per hour, find the time they reach Basecamp immediately.

i) How long did Olive stay in the shop?

ii) How far from her home is the shop?

iii) Compare the speed of her trip to the shop with her speed on the way home.

iv) Write a paragraph to describe her journey.

Join the Junior Cycle students using SimpleStudy...