A pastry shop and a flower shop, 500 m apart, are situated between Julie's house and Emily's house. The flower shop is halfway between the two houses
and the pastry shop is closer to Emily's house. Julie and Emily left their homes at the same time and arrived at the pastry shop at the same time. Julie drove at a speed of 77 km/h while Emily drove at a speed 14 km/h slower than Julie. Leaving your answer in kilometres,
- how much farther did Julie travel than Emily?
- how far is Emily's house from the flower shop?
(a)
Let the distance between Julie's house and Emily's house be 1 d.
Emily travelled =
12 d - 500 m
Julie travelled =
12 d + 500 m
Distance that Julie travelled more than Emily
=
12 d + 500 - (
12 d - 500)
=
12 d + 500 -
12 d + 500
= 1000 m
= 1 km
(b)
Time that Julie took to travel to the pastry shop
= 1 ÷ 14
=
114 h
Distance that Julie travelled
=
114 x 77
= 5.5 km
1000 m = 1 km
500 m = 0.5 km
Distance between Emily's house and the flower shop
= 5.5 - 0.5
= 5 km
Answer(s): (a) 1 km; (b) 5 km