Question

A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs \(\$ 1.25\) per gallon, how long will it take for the truck owner to refuel his vehicle with \(\$ 40\) worth of diesel fuel? A 20 seconds B 1 minute C 1 minute 20 seconds D 20 minutes E 1 hour 20 minutes

Short answer

The truck owner will take 1 minute 20 seconds to refuel the vehicle.

Step-by-step solution

- Determine the total gallons of diesel fuel

First, calculate how many gallons of diesel fuel can be bought with \(40. Given that the cost is \)1.25 per gallon, use the formula: \text{total gallons} = \frac{\text{\text{\text{amount}}= 40} \text{\text{\text{\text{\text{\text{\text}}}}}}}}}}}

- Determine the time required to refuel per gallon

Next, use the rate at which the truck owner refuels to find the total time needed. Since the rate is 2 gallons per 5 seconds, calculate the time taken for the total gallons obtained in Step 1.

- Convert the time into appropriate units

Finally, convert the total time into minutes and seconds to determine the correct answer from the provided options.

Key concepts

Understanding Word Problems

Word problems are math problems written in a narrative form. They require you to extract mathematical information from text. This particular problem involves calculating the time required to refuel a truck with diesel fuel given certain conditions.

To solve word problems effectively:

• Identify key information and numbers
• Understand what you need to find
• Translate words into mathematical equations or expressions

Extracting and using relevant data correctly can simplify even complex problems.

Rate Calculation

Rate calculations are essential in determining how fast or slow something happens over time. In this exercise, we need to find the refueling rate given in gallons per seconds:

The truck refuels at a rate of 2 gallons every 5 seconds. To find the rate in gallons per second, divide the gallons by the seconds:
\[ \frac{2 \text{ gallons}}{5 \text{ seconds}} = 0.4 \text{ gallons per second} \]
This rate will help us determine the total time needed for the refueling process.

Applying GMAT Math Strategies

GMAT math strategies are problem-solving techniques specifically designed for tackling standardized test questions efficiently. Here are some key strategies:

• Break problems into smaller steps
• Read questions carefully
• Use logical elimination to discard obviously incorrect answers
• Double-check your calculations

In this problem, start by calculating the total gallons needed, then determine the time for refueling, and finally convert units.

Fuel Cost Calculation

Fuel cost calculation requires knowing the cost per unit and the total expenditure. Here, we need to determine the total gallons of diesel bought for \$40 with the cost per gallon being \$1.25:

Use the formula: \[ \text{total gallons} = \frac{40 \text{ dollars}}{1.25 \text{ dollars per gallon}} = 32 \text{ gallons} \]
Knowing the total gallons, we can now proceed to calculate the time needed for refueling.

Time Conversion

Converting time from one unit to another is crucial for the final step. After finding the total refueling time using rate: \[ \text{time (in seconds)} = \frac{32 \text{ gallons}} {0.4 \text{ gallons/second}} = 80 \text{ seconds} \]
Convert these seconds into minutes and seconds:

• 1 minute = 60 seconds
• 80 seconds = 1 minute 20 seconds

Hence, the time taken will be 1 minute and 20 seconds, matching option C. Always ensure to convert time into appropriate units given in the answer choices.