A park and a museum, 1500 m apart, are situated between Yoko's house and Jaslyn's house. The museum is halfway between the two houses and the park is closer to Jaslyn's house. Yoko and Jaslyn left their homes at the same time and arrived at the park at the same time. Yoko drove at a speed of 67 km/h while Jaslyn drove at a speed 10 km/h slower than Yoko. Leaving your answer in kilometres,

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

(a)
Let the distance between Yoko's house and Jaslyn's house be 1 d.
Jaslyn travelled = ¹₂ d - 1500 m
Yoko travelled = ¹₂ d + 1500 m

Distance that Yoko travelled more than Jaslyn
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Yoko took to travel to the park
= 3 ÷ 10
= ³₁₀ h

Distance that Yoko travelled
= ³₁₀ x 67
= 20.1 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jaslyn's house and the museum
= 20.1 - 1.5
= 18.6 km

Answer(s): (a) 3 km; (b) 18.6 km