Before mechanic:
340 miles with 8 gallons.
A gallon costs $4, so 8 gallons cost 8 * $4 = $32.
$32 per 340 miles = $32/340 = $0.0941/mile = 9.4 cents/mile
After mechanic:
350 miles with 7 gallons.
7 gallons cost 7 * $4 = $28.
$28 per 350 miles = $28/350 = $0.08/mile = 8 cents/mile
The difference is 9.4 - 8 = 1.4.
To the nearest cent, round 1.4 to 1.
Answer: After the mechanic, it cost 1 cent per mile less to run the car.