Rate and Ratio：練習問題

A potting soil blend is made from peat moss, perlite, and compost in the ratio \(5:2:3\) by volume. If a nursery has \(220\) L of peat moss, \(80\) L of perlite, and \(150\) L of compost, what is the maximum amount of potting soil (in L) they can produce?

In a community centre, the ratio of the number of members in the Yoga class to the Dance class is \(3 : 4\). The ratio of the number of members in the Dance class to the Painting class is \(5 : 2\). If there are \(14\) more members in the Yoga class than in the Painting class, how many members are in the Dance class?

A concrete mix uses cement, sand, and gravel in the ratio \(1:2:4\) by weight. If a builder has \(85\) kg of cement, \(160\) kg of sand, and \(330\) kg of gravel, what is the maximum weight of concrete (in kg) they can produce according to this ratio?

A sports club has 20 footballs, 15 basketballs and 10 rugby balls. Find the ratio of the number of footballs to the number of basketballs to the number of rugby balls in its simplest form.

A factory has $$4$$ machines that can produce $$120$$ garments in $$8$$ hours. If $$6$$ machines are used to produce $$270$$ garments, how many hours will it take, assuming all machines operate at the same constant speed?

A car can travel \( 126 \text{ km} \) in \( 1.5 \text{ hours} \) at a constant speed. Calculate the average speed of the car in \( \text{km/h} \).

A car and a bus travel from Town P to Town Q at constant average speeds. The ratio of the average speed of the car to the average speed of the bus is \(5:4\). If the car departs \(30\) minutes after the bus but arrives \(15\) minutes before the bus, find the time taken by the bus for the journey in hours.

A floor plan for a new office is drawn using a scale of \( 1 : 50 \).

(a) The actual length of a conference room wall is \( 6.5 \text{ m} \). Calculate the length of this wall on the floor plan in \(\text{cm}\).
(b) On the floor plan, the width of a window is \( 3.2 \text{ cm} \). Find the actual width of the window in \(\text{m}\).
(c) If the floor plan is enlarged so that the new scale is \( 1 : 25 \), what would be the new length of the wall from part (a) on this enlarged plan in \(\text{cm}\)?

A water pump can discharge \( 4500 \text{ litres} \) of water in \( 1.5 \text{ hours} \) at a constant rate.

(a) Find the rate of water discharge in litres per minute (\(\text{L/min}\)).
(b) A swimming pool has a capacity of \( 120 \text{ m}^3 \). How many hours will it take for this pump to fill the pool completely? (Given: \( 1 \text{ m}^3 = 1000 \text{ litres} \))
(c) If a second pump with a discharge rate of \( 70 \text{ L/min} \) is also used, how many minutes will it take for both pumps working together to fill the same pool?