A park and a museum, 1500 m apart, are situated between Zara's house and Lucy's house. The museum is halfway between the two houses and the park is closer to Lucy's house. Zara and Lucy left their homes at the same time and arrived at the park at the same time. Zara drove at a speed of 61 km/h while Lucy drove at a speed 10 km/h slower than Zara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zara took to travel to the park
= 3 ÷ 10
= ³₁₀ h

Distance that Zara travelled
= ³₁₀ x 61
= 18.3 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Lucy's house and the museum
= 18.3 - 1.5
= 16.8 km

Answer(s): (a) 3 km; (b) 16.8 km