A salon and a cafe, 1500 m apart, are situated between Lucy's house and Erika's house. The cafe is halfway between the two houses and the salon is closer to Erika's house. Lucy and Erika left their homes at the same time and arrived at the salon at the same time. Lucy drove at a speed of 77 km/h while Erika drove at a speed 20 km/h slower than Lucy. Leaving your answer in kilometres,

1. how much farther did Lucy travel than Erika?
2. how far is Erika's house from the cafe?

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

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

(b)
Time that Lucy took to travel to the salon
= 3 ÷ 20
= ³₂₀ h

Distance that Lucy travelled
= ³₂₀ x 77
= 11.55 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Erika's house and the cafe
= 11.55 - 1.5
= 10.05 km

Answer(s): (a) 3 km; (b) 10.05 km