A salon and a cafe, 500 m apart, are situated between Jaslyn's house and Min's house. The cafe is halfway between the two houses and the salon is closer to Min's house. Jaslyn and Min left their homes at the same time and arrived at the salon at the same time. Jaslyn drove at a speed of 75 km/h while Min drove at a speed 10 km/h slower than Jaslyn. Leaving your answer in kilometres,

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

(a)
Let the distance between Jaslyn's house and Min's house be 1 d.
Min travelled = ¹₂ d - 500 m
Jaslyn travelled = ¹₂ d + 500 m

Distance that Jaslyn travelled more than Min
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Jaslyn took to travel to the salon
= 1 ÷ 10
= ¹₁₀ h

Distance that Jaslyn travelled
= ¹₁₀ x 75
= 7.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Min's house and the cafe
= 7.5 - 0.5
= 7 km

Answer(s): (a) 1 km; (b) 7 km