Sathish is going on a 2100-kilometer road trip with 2 friends, whom he will pick up 150 kilometers after he begins the trip and drop off when there are 150 kilometers remaining. The car consumes 6 liters of gas for every 100 kilometers, and gas costs $1.20 per liter. Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together. How much will Sathish pay for gas?

Question

Sathish is going on a 2100-kilometer road trip with 2 friends, whom he will pick up 150 kilometers after he begins the trip and drop off when there are 150 kilometers remaining. The car consumes 6 liters of gas for every 100 kilometers, and gas costs  $1.20 per liter. Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together. How much will Sathish pay for gas?

Bytelearn · Accepted Answer

Calculate Total Distance: Calculate the total distance Sathish will be alone in the car. He starts alone for the first 150 kilometers and will be alone for the last 150 kilometers. 150 km + 150 km = 300 kmCalculate Distance with Friends: Calculate the distance Sathish will travel with his friends. The total trip is 2100 kilometers, and he is alone for 300 kilometers, so the distance with friends is 2100 km - 300 km. 2100 km - 300 km = 1800 kmCalculate Total Gas Consumption: Calculate the total gas consumption for the trip. The car consumes 6 liters per 100 kilometers, so for 2100 kilometers, the consumption is (2100 km / 100 km) * 6 liters. (2100 km / 100 km) * 6 liters = 21 * 6 liters = 126 litersCalculate Gas Consumption Alone: Calculate the gas consumption for the distance Sathish is alone. For 300 kilometers, the consumption is (300 km / 100 km) * 6 liters. (300 km / 100 km) * 6 liters = 3 * 6 liters = 18 litersCalculate Gas Consumption with Friends: Calculate the gas consumption for the distance Sathish travels with his friends. From the total consumption of 126 liters, subtract the 18 liters Sathish uses alone. 126 liters - 18 liters = 108 litersCalculate Cost of Gas for Entire Trip: Calculate the cost of gas for the entire trip. The cost of gas is $1.20 per liter, so for 126 liters, the cost is 126 liters * $1.20/liter. 126 liters * $1.20/liter = $151.20Calculate Cost of Gas Alone: Calculate the cost of gas for the distance Sathish is alone. For 18 liters, the cost is 18 liters * $1.20/liter. 18 liters * $1.20/liter = $21.60Calculate Cost of Gas Split: Calculate the cost of gas Sathish will split with his friends. From the total cost of $151.20, subtract the $21.60 Sathish pays alone. $151.20 - $21.60 = $129.60Determine Sathish's Share: Determine Sathish's share of the cost when traveling with friends. Sathish and his 2 friends will split the $129.60 evenly, so each person's share is $129.60 / 3. $129.60 / 3 = $43.20Calculate Total Amount Paid: Calculate the total amount Sathish will pay for gas. Sathish pays $21.60 when he is alone and $43.20 for his share with friends. $21.60 + $43.20 = $64.80

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