Question 1205398
if the speed is increased, then it will take less time.
example:
v is the original speed.
it is increased by the ratio m:n
if it is increased, then m must be greater than v.


increase in a ratio means to multiply the original value by by a fraction where the numerator is greater than the denominator.


v * m/n is greater than v.


if the speed is increased, the time to get to the destination will be less.

note that these problems use the general formula of r * t = d.
r is the speed of the vehicle.
t is the time it takes the vehicle to get to the destination.
d is the distance to get to the destination.





example:


r*t=d becomes 5*5=25 when r = 5 and t = 5.
the rate of the vehicle is 5 kilometers per hour.
the time it takes to the destination is 5 hours.
the distance if 5 kilometers per hour * 5 hours = 25 kilometers.


if you multiply r by 5/2, then r = 5 * 5/2 = 25/2 = 12.5
the new speed of the vehicle becomes 12.5 kilometers per hour.


rt=d becomes 12.5 * t = 25
solve for t to get t = 25/12.5 = 2


speed was increased, therefore time was decreased.


in what ratio was the time changed?


see below.


the formula is R * T = D
when you increase the rate by m/n, then the formula becomes R * n/m * T = D
if you divide both sides of the formula by R, you get m/n * T = D/R
if you multiply both sides of the equation by n/m, you get T = D/R * n/m
so your answer for in what ratio is the time changed should be n/m.
in my example, the original value of t was 5.
after multiplying the rate by 5/2, t was then 2.
so t must have been multiplied by 2/5 because 5 * 2/5 = 2
if 5/2 was m/n, then 2/5 must be n/m.

let me know if if your have any questions.


theo