Question

Rates and Speed Calculas question

Answer 1

I don't know how do get the equation; I know that i will need to take the derivative of that equation etc though. Thank you!

Answer 2

Sorry i'm with another question. I will look at this when i return.

Answer 3

i think you need to start by connecting up mpg and mph. you have two different regions, with 40mph <=> 18mpg as the mid point

you should be able to get to \(mpg = -\frac{mph}{10} + 22\) and \(mpg = -\frac{mph}{5} + 26\) for mph's < and > 40mph.

you can then get a volume usage "gallon/hour" number if you divide mpg by mph which you can then add that to the constant 4g/h leakage due to the hole in tank to get total \(\frac{dV}{dt}\) .

this combined \(\frac{dV}{dt}\) you can integrate with initial value V(0) = 14 to arrive at V(t). the thing will stop when \(V(t_{final}) = 0\) so solve for \(t = t_{final}\) giving an expression terms of \(\dot x\), where \(\dot x\) is mph. by then it will have travelled \(\dot x \times t_{final}\); so you have an expression for distance in terms of \(\dot x\) which you can differentiate and solve to optimise \(\dot x\) .

it's ugly.