A park and a museum, 1000 m apart, are situated between Dana's house and Emma's house. The museum is halfway between the two houses and the park is closer to Emma's house. Dana and Emma left their homes at the same time and arrived at the park at the same time. Dana drove at a speed of 76 km/h while Emma drove at a speed 19 km/h slower than Dana. Leaving your answer in kilometres,

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

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

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

(b)
Time that Dana took to travel to the park
= 2 ÷ 19
= ²₁₉ h

Distance that Dana travelled
= ²₁₉ x 76
= 8 km

1000 m = 1 km
1000 m = 1 km

Distance between Emma's house and the museum
= 8 - 1
= 7 km

Answer(s): (a) 2 km; (b) 7 km