(b) Emily has a piece of fencing wire for the garden that is 240 m long. Emily cuts it into three pieces in the ratio 1 : 2 : 5
(i) What is the length of the longest piece of wire? (ii) What is the length of the shortest piece of wire?
6. Below are the details of an airline return ticket from Dublin to Boston for two adults and one child.
Departure: All times are local From Dublin (DUB) to Boston (BOS) Thursday
Depart Dublin(DUB) Arrive Boston (BOS)
(a)
Flight no. 137 10:00
Return: All times are local From Boston (BOS) to Dublin (DUB) Sunday
Depart Boston (BOS) Arrive Dublin (DUB)
Flight no. 138 06:20 17:20
(i) Local time in Boston is 5 hours behind local time in Dublin. The estimated flight time between these two cities is seven hours. Calculate the estimated time of arrival in Boston.
(ii) The distance from Dublin to Boston is 4 806 km. Calculate the average speed of the plane, in km/hr, to the nearest whole number.
(b) The family has €2 500 spending money. Given an exchange rate of €1 = $US 1⋅14, convert the €2 500 to US dollars.
(c) The family spends $US 1 580 on accommodation and meals. Calculate the percentage (to the nearest whole number) of the family’s spending money that this represents.
(d) The formula for converting temperature in Fahrenheit to Celsius is C = 5 (F − 32)________
9 , where C = temperature in Celsius and F = temperature in Fahrenheit.
Given the temperature in Boston on the day the family arrived was 74 degrees Fahrenheit, convert this temperature to degrees Celsius. Give your answer to the nearest whole number.
7. Ann and Rachel are running in a road race. The map shows the route of the race.
The race consists of four laps of the route. Ann and Rachel run clockwise along the route at a constant speed.
(a) Using the map, work out the length of the entire race. (b) Ann takes 3 minutes to run one kilometre. Rachel takes 6 minutes to run one kilometre. Copy and complete the table below.
Time (min)
Ann’s distance (km)
Rachel’s distance (km)
(c) Using the same axis and scale, draw a graph to represent each runner’s race. (d) Calculate the speed of each runner in kilometres per minute.
(e) Find the slope of each graph. What do you notice about the slope of each graph and the speed of each person?
(f) Write an expression to represent the distance covered by each runner after t minutes.
(g) What distance will each runner have completed after 1·5 hours? Hint: Convert the time into minutes.