Henry's bus can go just 12 miles on a gallon of gasoline. When he started his vacation, the gas tank of the bus was 5/6 full. Later when Henry had driven 336 miles, the gauge showed that the tank was still 3/5 full. If his "low on gas" light will come on when he has 1/15 of a tank remaining, how much farther can he go before seeing that light?


x/336 = (3/5 - 1/15)/(5/6 - 3/5)
x/336 = (8/15)/(7/30)
x/336 = 16/7
x = 336(16/7) = 768 miles
Is this right?

or

Is this right?
7/30 of the tank was spent going 336
miles. So the full tank should be able to provide 30/7 * 336 or 1440
miles.(It's a big tank). So 14/15 of the tank should take him 14/15 *
1440 miles = 1344 miles. Since he's already gone 336 miles, he has
1344-336 = 1008 miles to go.

Can you please tell me why which one is correct?
Thanks

Your first answer is correct. The second answer doesn't take into consideration that he started with his tank 5/6 full. It is true he can go 1440 miles on a full tank, but with 5/6 tank he can only go 5/6 X 1440 = 1200 miles. His light will come one at 1/15 of a tank, or 96 miles remaining. 1200 - 96 - 336 = 768

Or you can do it like that:

Full tank ---> 1440 miles
8/15 of tank (remaining fraction) ----> 1440 * 8/15 = 768 miles

:)