A park and a museum, 2000 m apart, are situated between Lynn's house and Zara's house. The museum is halfway between the two houses and the park is closer to Zara's house. Lynn and Zara left their homes at the same time and arrived at the park at the same time. Lynn drove at a speed of 76 km/h while Zara drove at a speed 19 km/h slower than Lynn. Leaving your answer in kilometres,

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

(a)
Let the distance between Lynn's house and Zara's house be 1 d.
Zara travelled = ¹₂ d - 2000 m
Lynn travelled = ¹₂ d + 2000 m

Distance that Lynn travelled more than Zara
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Lynn took to travel to the park
= 4 ÷ 19
= ⁴₁₉ h

Distance that Lynn travelled
= ⁴₁₉ x 76
= 16 km

1000 m = 1 km
2000 m = 2 km

Distance between Zara's house and the museum
= 16 - 2
= 14 km

Answer(s): (a) 4 km; (b) 14 km