A salon and a cafe, 2000 m apart, are situated between Tina's house and Jane's house. The cafe is halfway between the two houses and the salon is closer to Jane's house. Tina and Jane left their homes at the same time and arrived at the salon at the same time. Tina drove at a speed of 66 km/h while Jane drove at a speed 15 km/h slower than Tina. Leaving your answer in kilometres,

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

(a)
Let the distance between Tina's house and Jane's house be 1 d.
Jane travelled = ¹₂ d - 2000 m
Tina travelled = ¹₂ d + 2000 m

Distance that Tina travelled more than Jane
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Tina took to travel to the salon
= 4 ÷ 15
= ⁴₁₅ h

Distance that Tina travelled
= ⁴₁₅ x 66
= 17.6 km

1000 m = 1 km
2000 m = 2 km

Distance between Jane's house and the cafe
= 17.6 - 2
= 15.6 km

Answer(s): (a) 4 km; (b) 15.6 km