Question

The mileage of Puja’s vehicle is 21 miles per gallon, given that the average speed of the car is 50 miles per hour. The gas tank of the vehicle has 17 gallons of gas when she started the trip. Which of the following will represent the gallons of gas remaining in the tank t hours after the trip begins when the vehicle travels at the average speed of 50 miles per hour.
(a) $f(t)=17-\dfrac{21}{50t}$
(b) $f(t)=17-\dfrac{50t}{21}$
(c) $f(t)=\dfrac{17-50t}{21}$
(d) $f(t)=\dfrac{17-21t}{50}$

Answer 1

Hint: First try to find the fuel consumed in the period of t hours, when the vehicle is moving with the average speed of 50miles per hour and its mileage is 21 miles per gallon using the formula $\text{distance=speed}\times \text{time}$ . Once you get the volume of fuel consumed, subtract it from the total amount of fuel that was present at the starting of the journey to get the answer.

Complete step-by-step answer:
Let us first try to find the fuel consumed while Puja’s vehicle has travelled for t hours. It is given the average speed of the vehicle miles per hour and we know that $\text{distance=speed}\times \text{time}$ . So, the distance travelled in the first t hours is equal to 50t.
Now, it is given that the mileage is 21 miles per gallon, which means 1 gallon of fuel can make the vehicle cover a distance of 21 miles. So, the amount of fuel consumed to move a vehicle a distance of 50t is equal to $\dfrac{50t}{21}$ .
So, the amount of fuel left is given by the difference of the fuel available at the start of the journey and the amount consumed. This can be represented mathematically as:
$f(t)=17-\dfrac{50t}{21}$
Therefore, the answer to the above question is option (b).

Note: Be careful about the units which you are using in the solution, all the quantities which are dimensionally same must have the same units. You should also know that the formula $\text{distance=speed}\times \text{time}$ is only valid if the speed is constant and the acceleration of the body is zero. Here options (b) and (c) are similar, so in a hurry, do not make the silly mistake of choosing option (c) as the correct answer.