A park and a museum, 1500 m apart, are situated between Olivia's house and Tammy's house. The museum is halfway between the two houses and the park is closer to Tammy's house. Olivia and Tammy left their homes at the same time and arrived at the park at the same time. Olivia drove at a speed of 64 km/h while Tammy drove at a speed 20 km/h slower than Olivia. Leaving your answer in kilometres,

1. how much farther did Olivia travel than Tammy?
2. how far is Tammy's house from the museum?

(a)
Let the distance between Olivia's house and Tammy's house be 1 d.
Tammy travelled = ¹₂ d - 1500 m
Olivia travelled = ¹₂ d + 1500 m

Distance that Olivia travelled more than Tammy
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Olivia took to travel to the park
= 3 ÷ 20
= ³₂₀ h

Distance that Olivia travelled
= ³₂₀ x 64
= 9.6 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Tammy's house and the museum
= 9.6 - 1.5
= 8.1 km

Answer(s): (a) 3 km; (b) 8.1 km