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 kilometer 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?





ty if u help <3

Answer 1

Sathish has to pay $\ \text{ }64.8$ for the gas consumption while travelling on a $\text{2100 kilometers}$ road trip.

Further explanation:

On a $\text{2100 kilometers}$ road trip, Sathish is alone in his car for first $\text{150 kilometers}$ and the last $\text{150 kilometers}$ such that the total distance that Satish travelled alone is,

$\fbox{\begin\\150 + 150 = 300{\text{ kilometers}}\end{minispace}}$

So, the distance for which Sathish travels with his two friends is,

$\fbox{\begin\\2100 - 300 = 1800{\text{ kilometers}}\end{minispace}}$

The cost of one litre gas consumption is $\ \text{ }1.2$.

Since it is given that the car consumes $\text{6 litres}$ of gas for every $\text{100 kilometers}$ then the gas consumption for a kilometer is obtained as,

$\text{Gas consumed per kilometer}= \frac{6}{100}$

Therefore, when Sathish is travelling alone in his car, the gas consumption is obtained as shown below.

$\fbox{\begin{minispace} \\\text{Gas consumption when Sathish is alone=}\dfrac{6}{100}\times 300 = 18\text{ litres}\\\\\end{minispace}}$

Then the price for this journey will be owned by Sathish alone and is calculated as $\fbox{\begin{minispace} \\\\18\times 1.2\\\end{minispace}}$.

Now, for the remaining $\text{1800 kilometers}$ when Sathish is travelling with his two friends, the gas consumption is obtained as,

$\fbox{\begin{minispace} \\\\\text{Gas consumption when Sathish is with his two friends=}\dfrac{6}{100}\times 1800 = 108\text{ litres}\\\\\end{minispace}}$

The total price of gas consumption during the journey travelled by Sathish with his friends will be ${108}\times 1.2$.

Then the price of this journey will be divided among the three such that Sathish has to pay the amount calculated as $\fbox{\begin{minispace} \\\dfrac{108\times 1.2}{3}\\\end{minispace}}$.

Hence, the total amount that is to be paid by Sathish is,

$\text{Sathish's Share} = (18 \times 1.2) + 108 \times \left( 1.2 \times \dfrac{1}{3}\right)$

$\text{Sathish's Share} = 21.6 + (108 \times 0.4)$

$\text{Sathish's Share} = 21.6 + 43.2$

$\text{Sathish's Share} = 64.8$

Therefore, Sathish has to pay $\fbox{\begin\ \text{ }64.8\end{minispace}}$.

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Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Linear equation

Keywords:

pay, road trip, 150 kilometers, 300 kilometers, 2100 kilometers, gas consumption, Sathish, car, two friends, journey, distance, Sathish's share, trip, 6 litres.

Answer 2

Answer:

Step-by-step explanation:

$64.80