Hare

Time (minutes) | Distance (m) | 0-10 | 192 | 10-40 | 192 | 40-50 | 384 | 50-80 | 384 |

∴In 1 hour the hare travels 384m

Tortoise

Tortoise travels 5.4m per minute. There are 60 minutes in an hour.

∴Distance=5.4 ×60

=324

∴In 1 hour the tortoise travels 324m b) In 40mins hare travels 192m ×10=192m

In 40mins tortoise travels 5.4m ×40=216m

| Distance Travelled (m) | Time (Minutes) | Hare | Tortoise | 40 | 192 | 216 | 80 | 384 | 432 | 120 | 576 | 648 | 160 | 768 | 864 | 170 | 960 | 918 | 185.18518518 | 960 | 1000 | At 170 minutes, the Hare has just started his 30 minutes of sleeping and the tortoise has 82m of the race left.

Time it takes tortoise to travel 82m=82 ÷5.4

=15.185

The tortoise takes 15.185 minutes to complete the race after 918m, in this time the Hare is still sleeping.

1000-960=40

∴The Tortoise wins the race by 40 metres

c) If the tortoise maintained a hopping speed of 200m per minute, his pattern would be 200m of hopping the 30 minutes sleep. | Distance | Time (Minutes) | Hare | Tortoise | 40 | 200 | 216 | 80 | 400 | 432 | 120 | 600 | 648 | 160 | 800 | 864 | 170 | 1000 | 918 |

Looking at the table above, it can be seen that if the hare maintains a hopping speed of 20m per minute he can win the race and keep the same hopping pattern.

d) Looking at the table in question b, it appears that the tortoise is winning the whole race, however this is not the case and upon closer inspection. | Distance (m) | Time (Minutes) | Hare | Tortoise | 10 | 192 | 54 | 20 | 192 | 108 | 30 | 192 | 162 | 40 | 192 | 216 | 50 | 384 | 270 | 60 | 384 | 324 | 70 | 384 | 378 | 80 | 384 | 432 | 90 | 576 | 486 | 100 | 576 | 540 | 110 | 576 | 594 | 120 | 576 | 648 | 130 | 768 | 702 | 140 | 768 | 756 | 150 | 768 | 810 | 160 | 768 | 864 | 170 | 960 | 918 | 180 | 960 | 972 | 190 | 960 | 1026 | 200 | 960 | 1080 | 210 | 1152 | 1134 | 220 | 1152 | 1188 | 230 | 1152 | 1242 | 240 | 1152 | 1296 | 250 | 1344 | 1350 | 260 | 1344 | 1404 | 270 | 1344 | 1458 | 280 | 1344 | 1512 | 290 | 1536 | 1566 | 300 | 1536 | 1620 | 310 | 1536 | 1674 | 320 | 1536 | 1728 | 330 | 1728 | 1782 | 340 | 1728 | 1836 | 350 | 1728 | 1890 | 360 | 1728 | 1944 | 370 | 1920 | 1998 | 380 | 1920 | 2051 | 390 | 1920 | 2106 | 400 | 1920 | 2160 | 410 | 2112 | 2214 | 420 | 2112 | 2268 | 430 | 2112 | 2322 | 440 |…