A park and a museum, 500 m apart, are situated between Ivory's house and Penelope's house. The museum is halfway between the two houses and the park is closer to Penelope's house. Ivory and Penelope left their homes at the same time and arrived at the park at the same time. Ivory drove at a speed of 64 km/h while Penelope drove at a speed 16 km/h slower than Ivory. Leaving your answer in kilometres,

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

(a)
Let the distance between Ivory's house and Penelope's house be 1 d.
Penelope travelled = ¹₂ d - 500 m
Ivory travelled = ¹₂ d + 500 m

Distance that Ivory travelled more than Penelope
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Ivory took to travel to the park
= 1 ÷ 16
= ¹₁₆ h

Distance that Ivory travelled
= ¹₁₆ x 64
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Penelope's house and the museum
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km