A salon and a cafe, 1500 m apart, are situated between Erika's house and Barbara's house. The cafe is halfway between the two houses and the salon is closer to Barbara's house. Erika and Barbara left their homes at the same time and arrived at the salon at the same time. Erika drove at a speed of 71 km/h while Barbara drove at a speed 20 km/h slower than Erika. Leaving your answer in kilometres,

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

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

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

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

Distance that Erika travelled
= ³₂₀ x 71
= 10.65 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Barbara's house and the cafe
= 10.65 - 1.5
= 9.15 km

Answer(s): (a) 3 km; (b) 9.15 km