A park and a museum, 500 m apart, are situated between Usha's house and Yen's house. The museum is halfway between the two houses and the park is closer to Yen's house. Usha and Yen left their homes at the same time and arrived at the park at the same time. Usha drove at a speed of 62 km/h while Yen drove at a speed 10 km/h slower than Usha. Leaving your answer in kilometres,

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

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

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

(b)
Time that Usha took to travel to the park
= 1 ÷ 10
= ¹₁₀ h

Distance that Usha travelled
= ¹₁₀ x 62
= 6.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yen's house and the museum
= 6.2 - 0.5
= 5.7 km

Answer(s): (a) 1 km; (b) 5.7 km