A pharmacy and a bank, 2000 m apart, are situated between Raeann's house and Gabby's house. The bank is halfway between the two houses and the pharmacy is closer to Gabby's house. Raeann and Gabby left their homes at the same time and arrived at the pharmacy at the same time. Raeann drove at a speed of 65 km/h while Gabby drove at a speed 13 km/h slower than Raeann. Leaving your answer in kilometres,

1. how much farther did Raeann travel than Gabby?
2. how far is Gabby's house from the bank?

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

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

(b)
Time that Raeann took to travel to the pharmacy
= 4 ÷ 13
= ⁴₁₃ h

Distance that Raeann travelled
= ⁴₁₃ x 65
= 20 km

1000 m = 1 km
2000 m = 2 km

Distance between Gabby's house and the bank
= 20 - 2
= 18 km

Answer(s): (a) 4 km; (b) 18 km