Question

A tortoise and hare decide to run the 1000m dash. The tortoise manages to finish the whole race with

an average speed of 0.20 m/s. The hare, on the other hand, went much faster for the first 800m of the race, with
an average speed of 2.0 m/s. He was so far in the lead, that he decides to take a nap, and actually falls asleep for
1 hour 15 minutes. When he wakes up, he sees that the tortoise has pulled ahead of him! So the hare hurries to
the end of the race with an average speed of 1.5 m/s. Who wins the race and by how much time?

Answer 1

The tortoise won the race by approximately
`33\; {\rm s}`.

Step-by-step explanation:

Note that speed in the question is measured in meters-per-second. Apply unit conversion and ensure that times in this question are also measured in seconds:

`\begin{aligned} &1\; {\text{hour}} + 15\; {\text{minute}} \\ =\; & 1\; {\text{hour}} * \frac{3600\; {\rm s}}{1\; {\text{hour}}} + 15\; {\text{minute}} * \frac{60\; {\rm s}}{1\; \text{minute}} \\ =\; & 4500\; {\rm s}\end{aligned}`.

Time required for the tortoise to finish the race:

`\begin{aligned} \text{time} &= \frac{\text{distance}}{\text{speed}} \\ &= \frac{1000\; {\rm m}}{0.20\; {\rm m\cdot s^(-1)}} \\ &= 5000\; {\rm s}\end{aligned}`.

The time required for the hare to finish the race includes:

• time required to cover
  `800\; {\rm m}` at a speed of
  `2.0\; {\rm m\cdot s^(-1)}`,
• 
  `1\; \text{hour}` and
  `15\; \text{minute}` (
  `4500\; {\rm s}`) of nap, and
• time required to cover
  `(1000 - 800)\; {\rm m} = 200\; {\rm m}` at
  `1.5\; {\rm m\cdot s^(-1)}`.

`\begin{aligned} \frac{800\; {\rm m}}{2.0\; {\rm m\cdot s^(-1)}} + 4500\; {\rm s} + \frac{200\; {\rm m}}{1.5\; {\rm m\cdot s^(-1)}} \approx 5033\; {\rm s} \end{aligned}`.

Therefore, the tortoise wins the race by approximately
`5033\; {\rm s} - 5000\; {\rm s} = 33\; {\rm s}`.