(a)

Let walking speed = s

Riding speed is 3 times the walking speed.

Riding speed = 3 x s = 3s

Time for riding = 45 minutes = $\frac{45}{60}$ hours = $\frac{9}{12}$ hours

Distance travelled by riding = 3s x $\frac{9}{12}$ = $\frac{\mathrm{9s}}{4}$

Time for walking = 1 hour

Distance travelled by walking = s x 1 = s

Total distance covered = 10.4 km = 10.4 x 10³ m = 10400 m

Distance travelled by riding + Distance travelled by walking = 10400 m

$\frac{\mathrm{9s}}{4}$ + s = 10400

Get rid of the fraction by multiplying both sides by the denominator 4

4 x $\frac{\mathrm{9s}}{4}$ + s x 4 = 10400 x 4

9s + 4s = 41600

13s = 41600

Divide both sides by 13

s = $\frac{41600}{13}$ = 3200 m/hour

Walking speed = 3200 m/hour = 3.2 km/h

(b)

Distance travelled by riding = $\frac{\mathrm{9s}}{4}$

But s = 3200 m/hour

Distance travelled by riding = $\frac{\mathrm{9\; x\; 3200}}{4}$ = 7200 m = 7.2 km

(i)

Speed = 60 km/h

Time = 135 minutes = $\frac{135}{60}$ hours = 2.25 hours

Distance between Samoa and Mepeasem = 60 km/h x 2.25 h = 135.0 km (one decimal place)

(ii)

She took 3 minutes less to arrive at Samoa.

Return time = 135 minutes - 3 minutes = 132 minutes

Return time = $\frac{132}{60}$ hours = 2.2 hours

Speed = $\frac{\mathrm{Distance}}{\mathrm{Time}}$

Distance = 135 km

Return speed = $\frac{\mathrm{135\; km}}{\mathrm{2.2\; h}}$ = 61.35 km/h ≈ 61.4 km/h (one decimal place)