Question

pete is starting to drive his bus to los angeles. the bus has a full tank of gas containing 11 gallons. the bus is able to travel 38 miles per gallon of gas. it uses \\(\frac{1}{38}\\) of a gallon of gas to go 1 mile.
show your work here
how many miles can the bus travel before it needs to be refueled?
\\(\boxed{}\\) miles
the trip to los angeles takes 1596 miles. how many gallons of gas will pete need in total to make the trip to los angeles?
\\(\boxed{}\\) gallons
pete wants to refuel the bus the least amount of times as possible. starting with a full tank of gas, what is the minimum number of times pete will need to refuel the vehicle to make it to los angeles?
\\(\boxed{}\\) times

Explanation:

Step1: Calculate miles per full tank

The bus has 11 gallons, and travels 38 miles per gallon. So total miles per tank: $11 \times 38 = 418$ miles.

Step2: Calculate total gas for trip

Trip is 1596 miles, and gas usage is $\frac{1}{38}$ gallon per mile. So total gas: $1596 \times \frac{1}{38} = 42$ gallons.

Step3: Calculate refuel times

Full tank is 11 gallons. Total gas needed is 42 gallons. Initial tank: 11 gallons. Remaining gas needed: $42 - 11 = 31$ gallons. Each refuel is a full tank (11 gallons). Number of refuels: $\lceil \frac{31}{11}
ceil = 3$ (since $2 \times 11 = 22 < 31$, $3 \times 11 = 33 \geq 31$). But wait, initial tank is 11, so total tanks used: $\lceil \frac{42}{11}
ceil = 4$, minus initial 1: $4 - 1 = 3$? Wait, no: initial tank is 1, so number of refuels is total tanks - 1. Total tanks: $\lceil 42 / 11
ceil = 4$ (since $3 \times 11 = 33 < 42$, $4 \times 11 = 44 \geq 42$). So refuels: $4 - 1 = 3$. Wait, but let's check:

First tank: 11 gallons (418 miles). Then refuel 1: 11 (total 22, 836 miles). Refuel 2: 11 (total 33, 1254 miles). Refuel 3: 11 (total 44, 1672 miles which is more than 1596). Wait, but total gas needed is 42 gallons. So initial 11, then need 31 more. 31 / 11 = 2.818, so 3 refuels (since 2 refuels give 22, 11+22=33 <42; 3 refuels give 33, 11+33=44 ≥42). So refuel times: 3.

Wait, maybe better to do:

1. Miles before refuel: $11 \times 38 = 418$ miles.
2. Total gas: $1596 \div 38 = 42$ gallons.
3. Number of tanks needed: $42 \div 11 = 3.818...$, so 4 tanks (since we can't have partial tanks). Subtract initial tank: $4 - 1 = 3$ refuels.

Answer:

• Miles before refuel: $\boxed{418}$
• Total gas: $\boxed{42}$
• Refuel times: $\boxed{3}$