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