A salon and a cafe, 1500 m apart, are situated between Gwen's house and Jane's house. The cafe is halfway between the two houses and the salon is closer to Jane's house. Gwen and Jane left their homes at the same time and arrived at the salon at the same time. Gwen drove at a speed of 64 km/h while Jane drove at a speed 10 km/h slower than Gwen. Leaving your answer in kilometres,

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

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

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

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

Distance that Gwen travelled
= ³₁₀ x 64
= 19.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jane's house and the cafe
= 19.2 - 1.5
= 17.7 km

Answer(s): (a) 3 km; (b) 17.7 km