A salon and a cafe, 1500 m apart, are situated between Natalie's house and Shannon's house. The cafe is halfway between the two houses and the salon is closer to Shannon's house. Natalie and Shannon left their homes at the same time and arrived at the salon at the same time. Natalie drove at a speed of 69 km/h while Shannon drove at a speed 10 km/h slower than Natalie. Leaving your answer in kilometres,

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

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

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

(b)
Time that Natalie took to travel to the salon
= 3 ÷ 10
= ³₁₀ h

Distance that Natalie travelled
= ³₁₀ x 69
= 20.7 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Shannon's house and the cafe
= 20.7 - 1.5
= 19.2 km

Answer(s): (a) 3 km; (b) 19.2 km