SOLUTION: A train normally travels between two stations at v km/h. If its average speed is increased in the ratio m:n, will it take more or less time? In what ratio is the time changed?

Question 1205398: A train normally travels between two stations at v km/h. If its average speed is increased in the ratio m:n, will it take more or less time?
In what ratio is the time changed?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The question is not well written....

Since the distances are always the same, increasing the speed will decrease the time required. If the speed is increased by the ratio m:n, then the time required is DECREASED by the ratio m:n.

The question as written is "In what ratio is the time changed?". With that wording, the answer could be either m:n or n:m.

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