A salon and a cafe, 500 m apart, are situated between Barbara's house and Eva's house. The cafe is halfway between the two houses and the salon is closer to Eva's house. Barbara and Eva left their homes at the same time and arrived at the salon at the same time. Barbara drove at a speed of 74 km/h while Eva drove at a speed 20 km/h slower than Barbara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Barbara took to travel to the salon
= 1 ÷ 20
= ¹₂₀ h

Distance that Barbara travelled
= ¹₂₀ x 74
= 3.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Eva's house and the cafe
= 3.7 - 0.5
= 3.2 km

Answer(s): (a) 1 km; (b) 3.2 km