MathBrush

Practice

Same pattern as Aladdin and Jasmine — the magic carpet race. New numbers, new story. Try each one on paper, then check the working below — or watch it drawn out, the same way the problem above is.

Question 1

Two speedboats, the Dolphin and the Marlin, raced from the same jetty to an island. Both left at 08:00 and did not change their speed throughout the journey. The Dolphin travelled at a constant speed of 40 km/h. When it reached the island at 08:30, the Marlin was 2 km from the island. What was the Marlin's speed?

Work it out on paper, then check below. ▶ See the working

Question 2

Drone X and Drone Y raced from the same depot to deliver packages to a rooftop pad. Both launched at 10:00 and did not change their speed throughout the flight. Drone X flew at a constant speed of 72 km/h. When it reached the rooftop at 10:15, Drone Y was 3 km from the rooftop. What was Drone Y's speed?

Work it out on paper, then check below. ▶ See the working

Question 3

Two remote-control race cars, Car A and Car B, started from the same line on a track at 14:00. Both did not change their speed throughout the race. Car A travelled at a constant speed of 36 km/h. When it crossed the finish line at 14:20, Car B was 1.5 km from the finish line. What was Car B's speed?

Work it out on paper, then check below. ▶ See the working

The working

Question 1

  1. Find how long both boats had been travelling when the Dolphin arrived.08:30 − 08:00 = 30 min = 0.5 h
  2. Use the Dolphin's speed and time to find the distance from the jetty to the island.40 km/h × 0.5 h = 20 km
  3. Both boats travelled for the same half hour, so subtract the Marlin's remaining gap from that same distance to get how far the Marlin had gone.20 km − 2 km = 18 km
  4. Divide the Marlin's distance by the time to find its speed.18 km ÷ 0.5 h = 36 km/h

The Marlin's speed was 36 km/h.

The pattern. Same time, same distance: both boats travel for the same 0.5 h, so the leader's distance minus the trailing gap gives the other boat's distance directly.

Question 2

  1. Find how long both drones had been flying when Drone X arrived.10:15 − 10:00 = 15 min = 0.25 h
  2. Use Drone X's speed and time to find the distance from the depot to the rooftop.72 km/h × 0.25 h = 18 km
  3. Both drones flew for the same 15 minutes, so subtract Drone Y's remaining gap from that same distance to get how far Drone Y had gone.18 km − 3 km = 15 km
  4. Divide Drone Y's distance by the time to find its speed.15 km ÷ 0.25 h = 60 km/h

Drone Y's speed was 60 km/h.

The pattern. Same time, same distance: both drones fly for the same 0.25 h, so the leader's distance minus the trailing gap gives the other drone's distance directly.

Question 3

  1. Find how long both cars had been racing when Car A finished.14:20 − 14:00 = 20 min = 1/3 h
  2. Use Car A's speed and time to find the length of the track.36 km/h × 1/3 h = 12 km
  3. Both cars raced for the same 20 minutes, so subtract Car B's remaining gap from that same distance to get how far Car B had gone.12 km − 1.5 km = 10.5 km
  4. Divide Car B's distance by the time to find its speed.10.5 km ÷ 1/3 h = 31.5 km/h

Car B's speed was 31.5 km/h.

The pattern. Same time, same distance: both cars race for the same 1/3 h, so the leader's distance minus the trailing gap gives the other car's distance directly.