Let us assume the car's speed in first gear is x and in second gear is y.
From this, the car's speed in the fifth gear will be 5x. We are told that it takes twice the time to travel a certain distance in the second gear compared to the third gear. This means the car's speed in third gear is twice that of the car in second gear.
We are told that if a car travels an equal distance in each gear, for a total journey of 100km, it would take 585 minutes.
That is $\frac{25}{x}+\frac{25}{y}+\frac{25}{2y}+\frac{25}{5y}=585$
$\frac{5}{x}+\frac{5}{y}+\frac{5}{2y}+\frac{5}{5y}=117$
$\frac{\left(50y+50x+25x+10y\right)}{10xy}=117$
$\frac{75x+60y}{10xy}=117$
$\frac{5x+4y}{10xy}\cdot15=117$
$\frac{5x+4y}{2xy}\cdot3=117$
$\frac{5x+4y}{2xy}=39$
$\frac{5}{y}+\frac{4}{x}=78$
Next, we are asked to determine the time taken when thedistances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively.
T =$\frac{4}{x}+\frac{4}{y}+\frac{32}{2y}+\frac{60}{5x}$
T =$\frac{4}{x}+\frac{4}{y}+\frac{16}{y}+\frac{12}{x}$
T =$\frac{16}{x}+\frac{20}{y}$ =$4\left(\frac{4}{x}+\frac{5}{y}\right)$ =$4\cdot78\ =\ 312\ \text{mins }$
