Problem Solving

alex.gellatly wrote:At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

A) 3/25
B) 11/36
C) 7/12
D) 2/3
E) 25/36

Thanks in advanced

Distance = speed * time
Distance = 50 miles
Time = 5 hours
Distance traveled by car per hour = 5 * 50 = 250 miles
So, the care will use 250/30 = 25/3 gallons of gasoline.
Gasoline used/full tank = (25/3)/12 = [spoiler]25/36[/spoiler]

The correct answer is E.

alex.gellatly wrote:At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

A) 3/25
B) 11/36
C) 7/12
D) 2/3
E) 25/36

So far, the posts have used the ratio (consumption)/(distance traveled).
We can also use the ratio (consumption)/(time elapsed).

At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles.
Time = distance/speed
So, time to travel 30 miles = 30/50 = 3/5 hours.
This means that the car uses 1 gallon for every 3/5 hours.

Let x = the number of gallons of gas used during the 5 hour trip.

We get the following equivalent ratios: 1/(3/5) = x/ 5
Cross multiply to get: 5 = (3/5)x
Multiply both sides by 5/3 to get: 25/3 = x
So, the car uses 25/3 gallons of gas

The amount of gasoline used would be what fraction of a full tank?
We get (25/3)/12, which equals [spoiler]25/36[/spoiler]

Answer: E

Cheers,
Brent

alex.gellatly wrote:At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

A) 3/25
B) 11/36
C) 7/12
D) 2/3
E) 25/36

We are given that a certain car has a rate of 30 miles per gallon. We are next told that the car starts with a 12-gallon tank and travels for 5 hours at 50 miles per hour.

Since distance = rate x time, we know the car traveled 50 x 5 = 250 miles. We can use the car's rate and distance traveled to determine how many gallons were used.

Gallons used = distance/rate

Gallons used = 250/30 = 25/3

Finally, we need to determine the amount of gasoline used as a fraction of a full 12-gallon tank.

(25/3)/12 = (25/3) x (1/12) = 25/36

Answer: E