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

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

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

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

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

Distance that Usha travelled
= ⁴₁₅ x 66
= 17.6 km

1000 m = 1 km
2000 m = 2 km

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

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