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Q6 Steve leaves home at 11:15am. He drives at an average speed of 60mph for 45 minutes. He then stops for...

Q6 Steve leaves home at 11:15am. He drives at an average speed of 60mph for 45 minutes. He then stops for 45 minutes.
Steve then sets off home and arrives at 14:00.
[a] Draw the distance-time graph for Steve’s journey.
[b] What was Steve’s average speed on his way home?
[c] How far did Steve travel in total?
Q7 A fishing vessel travels a distance of 6 nautical miles at a speed of 8 knots. It then anchors for one hour, before travelling a further 5 nautical miles, in 45 minutes, to the next fishing ground. It anchors for 30 minutes before sailing 1 hour back to port.
1 knot = 1 nautical mile per hour.
[a] Draw the distance-time graph for the fishing vessel.
[b] What was the vessel’s average speed for the entire journey?

Answer

Q6 [a] Plot time horizontally and distance from home (miles) vertically. Join these points with straight lines: (11:15, 0), (12:00, 45), (12:45, 45), (14:00, 0). The outward distance is 60 × 45/60 = 45 miles.

Q6 [b] The return takes 1 hour 15 minutes = 1.25 hours. Average speed = 45 ÷ 1.25 = 36 mph.

Q6 [c] Total distance = 45 + 45 = 90 miles.

Q7 [a] Plot elapsed time (hours) horizontally and distance from port (nautical miles) vertically. The first leg takes 6 ÷ 8 = 0.75 hours. Join these points with straight lines: (0, 0), (0.75, 6), (1.75, 6), (2.5, 11), (3, 11), (4, 0).

Q7 [b] Total distance = 6 + 5 + 11 = 22 nautical miles. Total time, including stops, = 0.75 + 1 + 0.75 + 0.5 + 1 = 4 hours. Average speed = 22 ÷ 4 = 5.5 knots.

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