A park and a museum, 1500 m apart, are situated between Gillian's house and Kimberly's house. The museum is halfway between the two houses and the park is closer to Kimberly's house. Gillian and Kimberly left their homes at the same time and arrived at the park at the same time. Gillian drove at a speed of 68 km/h while Kimberly drove at a speed 17 km/h slower than Gillian. Leaving your answer in kilometres,

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

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

Distance that Gillian travelled more than Kimberly
= 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 ÷ 17
= ³₁₇ h

Distance that Gillian travelled
= ³₁₇ x 68
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kimberly's house and the museum
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km