A salon and a cafe, 3500 m apart, are situated between Victoria's house and Opal's house. The cafe is halfway between the two houses and the salon is closer to Opal's house. Victoria and Opal left their homes at the same time and arrived at the salon at the same time. Victoria drove at a speed of 60 km/h while Opal drove at a speed 20 km/h slower than Victoria. Leaving your answer in kilometres,

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

(a)
Let the distance between Victoria's house and Opal's house be 1 d.
Opal travelled = ¹₂ d - 3500 m
Victoria travelled = ¹₂ d + 3500 m

Distance that Victoria travelled more than Opal
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Victoria took to travel to the salon
= 7 ÷ 20
= ⁷₂₀ h

Distance that Victoria travelled
= ⁷₂₀ x 60
= 21 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Opal's house and the cafe
= 21 - 3.5
= 17.5 km

Answer(s): (a) 7 km; (b) 17.5 km