A park and a museum, 1500 m apart, are situated between Gillian's house and Kylie's house. The museum is halfway between the two houses and the park is closer to Kylie's house. Gillian and Kylie left their homes at the same time and arrived at the park at the same time. Gillian drove at a speed of 77 km/h while Kylie drove at a speed 11 km/h slower than Gillian. Leaving your answer in kilometres,

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

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

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

(b)
Time that Gillian took to travel to the park
= 3 ÷ 11
= ³₁₁ h

Distance that Gillian travelled
= ³₁₁ x 77
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kylie's house and the museum
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km