A park and a museum, 1500 m apart, are situated between Sarah's house and Opal's house. The museum is halfway between the two houses and the park is closer to Opal's house. Sarah and Opal left their homes at the same time and arrived at the park at the same time. Sarah drove at a speed of 77 km/h while Opal drove at a speed 14 km/h slower than Sarah. Leaving your answer in kilometres,

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

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

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

(b)
Time that Sarah took to travel to the park
= 3 ÷ 14
= ³₁₄ h

Distance that Sarah travelled
= ³₁₄ x 77
= 16.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Opal's house and the museum
= 16.5 - 1.5
= 15 km

Answer(s): (a) 3 km; (b) 15 km