A salon and a cafe, 2500 m apart, are situated between Nora's house and Kathy's house. The cafe is halfway between the two houses and the salon is closer to Kathy's house. Nora and Kathy left their homes at the same time and arrived at the salon at the same time. Nora drove at a speed of 68 km/h while Kathy drove at a speed 16 km/h slower than Nora. Leaving your answer in kilometres,

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

(a)
Let the distance between Nora's house and Kathy's house be 1 d.
Kathy travelled = ¹₂ d - 2500 m
Nora travelled = ¹₂ d + 2500 m

Distance that Nora travelled more than Kathy
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Nora took to travel to the salon
= 5 ÷ 16
= ⁵₁₆ h

Distance that Nora travelled
= ⁵₁₆ x 68
= 21.25 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Kathy's house and the cafe
= 21.25 - 2.5
= 18.75 km

Answer(s): (a) 5 km; (b) 18.75 km