Rates, speed & time

A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?

• A60 mph✓
• B55 mph
• C50 mph
• D65 mph

Answer: Speed = distance ÷ time = 150 ÷ 2.5 = 60 mph.

A printer produces 24 pages per minute. How many pages does it produce in 15 minutes?

• A300
• B320
• C360✓
• D400

Answer: 24 × 15 = 360 pages.

A train travels at 80 km/h. How far does it travel in 45 minutes?

• A60 km✓
• B65 km
• C50 km
• D55 km

Answer: 45 minutes = 0.75 hours; 80 × 0.75 = 60 km.

A worker is paid £14 per hour. How much does the worker earn for a 37.5-hour week?

• A£525✓
• B£540
• C£560
• D£500

Answer: £14 × 37.5 = £525.

A cyclist covers 36 km in 90 minutes. What is the average speed in km/h?

• A24 km/h✓
• B22 km/h
• C20 km/h
• D27 km/h

Answer: 90 minutes = 1.5 hours; 36 ÷ 1.5 = 24 km/h.

Three machines together fill 1,800 bottles per hour at the same rate each. How long would two of these machines take to fill 2,400 bottles?

• A1.5 hours
• B3 hours
• C2.5 hours
• D2 hours✓

Answer: Each machine fills 600/hour; two fill 1,200/hour; 2,400 ÷ 1,200 = 2 hours.

A car uses fuel at 6.5 litres per 100 km. How much fuel is needed for a 240 km journey?

• A16.2 litres
• B14.6 litres
• C15.6 litres✓
• D16.9 litres

Answer: 6.5 × (240 ÷ 100) = 6.5 × 2.4 = 15.6 litres.

A driver covers the first 120 km at 60 km/h and the next 120 km at 40 km/h. What is the average speed for the whole 240 km journey?

• A44 km/h
• B50 km/h
• C52 km/h
• D48 km/h✓

Answer: Time = 120/60 + 120/40 = 2 + 3 = 5 hours; 240 ÷ 5 = 48 km/h.

If 5 workers build a wall in 12 days, how long would 8 workers take, working at the same rate?

• A6 days
• B7.5 days✓
• C9 days
• D8 days

Answer: Total work = 5 × 12 = 60 worker-days; 60 ÷ 8 = 7.5 days.

A tap fills a tank in 6 hours; a drain empties it in 9 hours. With both open, how long to fill the empty tank?

• A18 hours✓
• B16 hours
• C21 hours
• D15 hours

Answer: Net rate = 1/6 - 1/9 = 3/18 - 2/18 = 1/18 per hour, so 18 hours.

A flight departs at 09:45 and lands at 14:20. How long was the flight?

• A4 hours 35 mins✓
• B4 hours 45 mins
• C5 hours 5 mins
• D4 hours 25 mins

Answer: From 09:45 to 14:45 is 5 hours; subtract 25 minutes gives 4 hours 35 minutes.

A pump moves 450 litres in 5 minutes. At this rate, how many litres does it move in one hour?

• A6,000 litres
• B5,800 litres
• C4,800 litres
• D5,400 litres✓

Answer: 450 ÷ 5 = 90 litres/min; 90 × 60 = 5,400 litres/hour.

Two trains start 360 km apart and travel towards each other at 90 km/h and 70 km/h. After how long do they meet?

• A2.25 hours✓
• B2.5 hours
• C2 hours
• D3 hours

Answer: Closing speed = 160 km/h; 360 ÷ 160 = 2.25 hours.

A train timetable shows a 165-mile journey scheduled for 2 hours 45 minutes. What is the average speed in mph?

• A55 mph
• B62 mph
• C58 mph
• D60 mph✓

Answer: 2 hours 45 minutes = 2.75 hours; 165 ÷ 2.75 = 60 mph.

A worker completes 3/8 of a project in 6 days. Working at the same rate, how many more days are needed to finish the remaining work?

• A14 days
• B10 days✓
• C8 days
• D12 days

Answer: 6 days = 3/8, so 1/8 = 2 days; the remaining 5/8 takes 5 × 2 = 10 days.