A park and a museum, 500 m apart, are situated between Kathy's house and Usha's house. The museum is halfway between the two houses and the park is closer to Usha's house. Kathy and Usha left their homes at the same time and arrived at the park at the same time. Kathy drove at a speed of 77 km/h while Usha drove at a speed 14 km/h slower than Kathy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Kathy took to travel to the park
= 1 ÷ 14
= ¹₁₄ h

Distance that Kathy travelled
= ¹₁₄ x 77
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Usha's house and the museum
= 5.5 - 0.5
= 5 km

Answer(s): (a) 1 km; (b) 5 km