Problem Solving: Time/Rate Flashcards

A clock gains 5 minutes every hour. Set correctly at noon, what time does the clock display when the real time is 4:00 PM?

Answer: 4:20 PM

In 4 real hours the clock gains 4 × 5 = 20 extra minutes, so it shows 4:00 PM + 20 min = 4:20 PM.

A 400 m long train passes a stationary observer in 20 seconds. How long does it take to pass through a tunnel 600 m long?

Answer: 50 seconds

Speed = 400 ÷ 20 = 20 m/s; total distance = 400 + 600 = 1,000 m; time = 1,000 ÷ 20 = 50 s.

Pipe A fills a tank in 4 hours, Pipe B in 6 hours, and Pipe C drains it in 12 hours. With all three open, how long to fill the empty tank?

Answer: 3 hours

Net rate = 1/4 + 1/6 − 1/12 = 3/12 + 2/12 − 1/12 = 4/12 = 1/3 per h; time = 3 hours.

A soldier marches at 6 km/h for 2 hours, then at 4 km/h for 3 hours. What is his average speed for the entire march?

Answer: 4.8 km/h

Total distance = 12 + 12 = 24 km; total time = 5 h; average = 24 ÷ 5 = 4.8 km/h.

Two cyclists 180 km apart ride toward each other at 30 km/h and 24 km/h. How far has the faster cyclist travelled when they meet?

Answer: 100 km

Meeting time = 180 ÷ 54 = 10/3 h; faster cyclist = 30 × 10/3 = 100 km.

A speedboat covers 120 km downstream in 2 hours and 120 km upstream in 3 hours. What is the boat's speed in still water?

Answer: 50 km/h

Downstream = 60 km/h, upstream = 40 km/h; still-water speed = (60 + 40) ÷ 2 = 50 km/h.

A task requires 108 worker-days. With 6 workers, it takes 18 days. After 6 days, 3 extra workers join. How many more days are needed to finish?

Answer: 8 days

Work done in 6 days = 6 × 6 = 36 worker-days; remaining = 72; with 9 workers = 72 ÷ 9 = 8 days.