A park and a museum, 1000 m apart, are situated between Cathy's house and Barbara's house. The museum is halfway between the two houses and the park is closer to Barbara's house. Cathy and Barbara left their homes at the same time and arrived at the park at the same time. Cathy drove at a speed of 69 km/h while Barbara drove at a speed 15 km/h slower than Cathy. Leaving your answer in kilometres,

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

(a)
Let the distance between Cathy's house and Barbara's house be 1 d.
Barbara travelled = ¹₂ d - 1000 m
Cathy travelled = ¹₂ d + 1000 m

Distance that Cathy travelled more than Barbara
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Cathy took to travel to the park
= 2 ÷ 15
= ²₁₅ h

Distance that Cathy travelled
= ²₁₅ x 69
= 9.2 km

1000 m = 1 km
1000 m = 1 km

Distance between Barbara's house and the museum
= 9.2 - 1
= 8.2 km

Answer(s): (a) 2 km; (b) 8.2 km