Sec 3 E-Math Ratio, Rate & Speed topical questions

Simplify 1.8 : 0.06.

Simplify 3/4 : 5/8.

$96 is shared between Amir and Beth in the ratio 5 : 3. Find each share.

Convert 90 km/h to m/s.

A photo measures 8 cm across on a 1 : 5 enlargement sheet. Find the real width, and the area factor between the sheet and the real photo.

A 3.5 m rope is cut into two pieces in the ratio 4 : 3. Find the length of each piece.

Convert 25 m/s to km/h.

A fruit seller packs 240 oranges into bags for two stalls in the ratio 7 : 5. (a) How many oranges go to each stall? (b) After delivery, the first stall returns 24 oranges to the seller, who gives them to the second stall. State the new ratio of oranges, in simplest form.

1. (a)Find the two original shares.[3]
2. (b)State the new ratio in simplest form.[3]

On a map with scale 1 : 20 000, a rectangular field measures 3.5 cm by 2 cm. Find (a) the real dimensions of the field in metres, (b) the real area in m², and (c) the area of the field on the map in cm².

1. (a)Real dimensions in metres.[2]
2. (b)Real area in m².[2]
3. (c)Map area in cm².[3]

Eight machines fill an order in 15 days. How long do six machines take, working at the same rate?

A hiker walks 14 km in 2 h 30 min. Find the average speed in (a) km/h and (b) m/s, correct to 3 significant figures.

1. (a)Average speed in km/h.[2]
2. (b)Average speed in m/s.[3]

A cyclist rides 24 km at 18 km/h, rests 20 minutes, then rides 12 km at 12 km/h. Find the average speed for the whole outing, correct to 3 significant figures.

On a map of scale 1 : 150 000, a nature reserve is a rectangle measuring 4.2 cm by 2.5 cm. Find (a) the real perimeter of the reserve in km, and (b) the real area of the reserve in km², correct to 3 significant figures.

1. (a)Real perimeter in km.[2]
2. (b)Real area in km².[3]

A taxi charges a $3.20 flag-down fee plus 55 cents for every completed 400 m of distance. Find the fare for a journey of 6.4 km.

A sum of money is shared between Kai and Lin in the ratio 4 : 7. After Kai gives Lin $18, the ratio becomes 1 : 2. Find the original amounts.

A map is drawn to a scale of 1 : n. A reservoir of real area 8 km² appears on the map with area 1.28 cm². (a) Find n. (b) A second reservoir of real area 5 km² is drawn on the same map. Find its map area.

Car A travels from Town P to Town Q at 64 km/h and takes 45 minutes. Car B travels the same route at 90 km/h. (a) Find the distance P Q. (b) How many minutes does Car B save?

Three friends rent a booth for $1 260. Anand pays 2 parts, Bela pays 3 parts and Chen pays 4 parts. (a) Find each person’s share. (b) Chen drops out and his share is split between Anand and Bela in the ratio 2 : 3. State each person’s new payment and the ratio of Anand’s to Bela’s payment, in simplest form.

1. (a)Find the three original shares.[3]
2. (b)Find the new payments and the new Anand : Bela ratio.[4]

A fruit stall has red and green apples in the ratio 5 : 8. After 45 red apples are sold, the ratio of red to green apples becomes 2 : 5. Find the number of green apples.

A shuttle travels 45 km on an expressway at 90 km/h, then 12 km on town roads at 48 km/h, and rests 15 minutes at a depot. Find (a) the total journey time, (b) the average speed for the whole journey in km/h, and (c) the average speed in m/s, correct to 3 significant figures.

1. (a)Total journey time.[2]
2. (b)Average speed in km/h.[2]
3. (c)Average speed in m/s (3 s.f.).[2]