A lawn mower manufacturer claims that one of its new gas-powered lawn mowers will run for 2 hours and 40 minutes on 1 quart of gasoline. If the claim is true, how long should this lawn mower run on 3 1/2 quarts of gasoline? [40 minutes is 2/3 of an hour.]
Group of answer choices
8 1/2 hours [or 8 hours and 30 minutes]
12 2/3 hours [or 12 hours and 40 minutes]
8 1/3 hours [or 8 hours and 20 minutes]
9 1/3 hours [or 9 hours and 20 minutes]
To find how long the lawn mower should run on 3 1/2 quarts of gasoline, we can use ratios.
If the mower runs for 2 hours and 40 minutes on 1 quart of gasoline, then we can set up a ratio of time to gasoline:
(2 hours + 40 minutes) : 1 quart = x hours : 3 1/2 quart
Converting 40 minutes to hours, we have:
(2+(40/60)) hours : 1 quart = x hours : 3 1/2 quart
Simplifying, we get:
(2+(2/3)) hours : 1 quart = x hours : 7/2 quart
Now, we can cross multiply:
(8/3) hours * (7/2) quart = x hours * 1 quart
Multiplying, we get:
(56/6) hours * quart = x hours * quart
Dividing both sides by quart, we get:
56/6 hours = x hours
Simplifying, we get:
x ≈ 9 1/3 hours
Therefore, the lawn mower should run for approximately 9 1/3 hours on 3 1/2 quarts of gasoline.
Answer: 9 1/3 hours [or 9 hours and 20 minutes]