**What is the 'slowest speed' that Shamus has to ride the bicycle so that he could catch up with Grace?**

Note: The units we are dealing here are: Time in minutes & Distance in metres.

Speed therefore is metres per minute (m/min). We'll have to convert it to something that is more common (i.e. m/s or km/h)

By answering to the pointers in the original question...

*What information do you know from the problem?**What else do you need to know to solve the problem?**Pick a reasonable number for the information you need.*

- The ratio of speed (one is 3 times the other)
- Maximum distance covered: 800 m
- One started the journey 10 minutes later

3. By using the info given, we can solve the problem using Algebra:

Let Grace's speed be x m/min

Shamus' speed is therefore 3x m/min

Since distance travelled = 800m (imagine that Shamus catches up with Grace at the school gate)

Time taken by Grace = 800/x min

Time taken by Shamus = 800/(3x) min

Since the time difference is 10 min (as Grace started earlier)

Time taken by Grace - Time taken by Shamus = 10

800/x - 800/(3x) = 10

by solving the algebraic equation, we have x = 53 1/3 m/min

To convert it to m/s, we have x = 8/9 m/min which is the same as 0.889 m/s (correct to 3SF)

Shamus takes 5 min to catch up with Grace

Therefore, time they meet = 6.45 am

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