Tummy Ache
Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?
Problem
Timmy, Tammy and Tommy all set off separately to visit their doctor, leaving their homes at exactly the same time.
Timmy cycles the 8 km at an average speed of 20 km/hr.
Tammy walks the 1.2 km at an average speed of 4 km/hr.
Tommy drives the 16.5 km at an average speed of 45 km/hr.
In what order do they arrive at the doctor's surgery?
Student Solutions
Answer: Tammy (first), Tommy, Timmy (last)
In hours
Timmy 8 km 20 km/h $\frac8{20}=\frac25$ of an hour
Tammy 1.2 km 4 km/h $\frac{1.2}{4} = \frac{12}{40} = \frac{3}{10}$ of an hour
Tommy 16.5 km 45 km/h $\frac{16.5}{45} = \frac{5.5\times3}{15\times3}=\frac{11}{30}$ not a nice fraction
compare $\frac25 = \frac{12}{30}$
$\frac{3}{10} = \frac{9}{30}$
$\therefore\frac{11}{30}$ middle
In minutes
Timmy 8 km 20 km/h $\frac1{3}$ km/minute 8$\times$3 = 24 minutes
Tammy 1.2 km 4 km/h $\frac{4}{60} = \frac{1}{15} $ km/minute 1.2$\times$15 = 18 minutes
Tommy 16.5 km 45 km/h $\frac{45}{60} = \frac{3}{4}$ km/minute 16.5$\div$3$\times$4 = 5.5$\times$4 = 22 minutes