A park and a museum, 500 m apart, are situated between Elyse's house and Yen's house. The museum is halfway between the two houses and the park is closer to Yen's house. Elyse and Yen left their homes at the same time and arrived at the park at the same time. Elyse drove at a speed of 72 km/h while Yen drove at a speed 12 km/h slower than Elyse. Leaving your answer in kilometres,

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

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

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

(b)
Time that Elyse took to travel to the park
= 1 ÷ 12
= ¹₁₂ h

Distance that Elyse travelled
= ¹₁₂ x 72
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yen's house and the museum
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km