Tanya and Naomi are roommates who are moving from Winnipeg t

Tanya and Naomi are roommates who are moving from Winnipeg to Calgary. They each own cars that they are using to move, but they decide to drive out together at the same time. Tanya\'s car gets 19 kilometers per litre of gasoline and Naomi\'s car gets 16 kilometers per litre of gasoline. When travelling from their own apartment in Winnipeg to their new place in Calgary, they both used a whole number of litres of gasoline. Assuming that the distance from Winnipeg to Calgary is between 1000 km and 1500 km, what is the exact distance they travelled on the trip?

Solution

We know that the distance between 1000 and 1500 km has to be a multiple of 19 and 16, or a multiple of 19*16 = 304; Let x be the multiplier of 304
:
304x > 1000
x > 1000/304
x > 3.3
and
304x < 1500
x < 1500/304
x < 4.9
:
Multiplier has to be 4: 4*304 = 1216 km is the distance
:
Tanya used: 1216/19 = 64 litres of gas
Naomi used: 1216/16 = 76 litres