A salon and a cafe, 3500 m apart, are situated between Olivia's house and Jade's house. The cafe is halfway between the two houses and the salon is closer to Jade's house. Olivia and Jade left their homes at the same time and arrived at the salon at the same time. Olivia drove at a speed of 62 km/h while Jade drove at a speed 20 km/h slower than Olivia. Leaving your answer in kilometres,

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

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

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

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

Distance that Olivia travelled
= ⁷₂₀ x 62
= 21.7 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Jade's house and the cafe
= 21.7 - 3.5
= 18.2 km

Answer(s): (a) 7 km; (b) 18.2 km