A salon and a cafe, 1000 m apart, are situated between Gwen's house and Kathy's house. The cafe is halfway between the two houses and the salon is closer to Kathy's house. Gwen and Kathy left their homes at the same time and arrived at the salon at the same time. Gwen drove at a speed of 63 km/h while Kathy drove at a speed 15 km/h slower than Gwen. Leaving your answer in kilometres,

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

(a)
Let the distance between Gwen's house and Kathy's house be 1 d.
Kathy travelled = ¹₂ d - 1000 m
Gwen travelled = ¹₂ d + 1000 m

Distance that Gwen travelled more than Kathy
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Gwen took to travel to the salon
= 2 ÷ 15
= ²₁₅ h

Distance that Gwen travelled
= ²₁₅ x 63
= 8.4 km

1000 m = 1 km
1000 m = 1 km

Distance between Kathy's house and the cafe
= 8.4 - 1
= 7.4 km

Answer(s): (a) 2 km; (b) 7.4 km