A pharmacy and a bank, 1500 m apart, are situated between Vanessa's house and Jade's house. The bank is halfway between the two houses and the pharmacy is closer to Jade's house. Vanessa and Jade left their homes at the same time and arrived at the pharmacy at the same time. Vanessa drove at a speed of 76 km/h while Jade drove at a speed 19 km/h slower than Vanessa. Leaving your answer in kilometres,

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

(a)
Let the distance between Vanessa's house and Jade's house be 1 d.
Jade travelled = ¹₂ d - 1500 m
Vanessa travelled = ¹₂ d + 1500 m

Distance that Vanessa travelled more than Jade
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Vanessa took to travel to the pharmacy
= 3 ÷ 19
= ³₁₉ h

Distance that Vanessa travelled
= ³₁₉ x 76
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jade's house and the bank
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km