Question

75 POINTS Need an immediate answer please brainliest will be given! A train left a station travelling to a city at 30 mph. The train traveled 1/3 of the distance at 30 mph and the remaining distance at 40 mph. Two hours later a car left the same station and traveled in the same direction to the same city. The car traveled the first 3 hours at 35 mph and the remaining distance at 51 mph. Knowing that they both reached the city at the same time, find the distance between the station and the city in terms of miles.

Answer 1

The value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

What is the rate of speed?

The rate of speed is the rate at which the total distance is travelled in the time taken. Rate of speed can be given as,

r=d/t

Here, (d) is the distance travelled by the object and (t) is time taken but the object to cover that distance.

The train traveled 1/3 of the distance at 30 mph and the remaining distance at 40 mph. Let t is the time the train has taken to travel and x is the distance it travelled. Thus,

$t=\dfrac{\dfrac{1}{3}x}{30}+\dfrac{\dfrac{2}{3}x}{40}\\t=\dfrac{x}{90}+\dfrac{x}{60}\\t=\dfrac{2x+3x}{180}\\t=\dfrac{5x}{180}\\t=\dfrac{x}{36}$

After two hour a car left the same station traveled the first 3 hours at 35 mph and the remaining distance at 51 mph. Let t is the time the car has taken to travel and x is the distance it travelled. Thus,

$t+2=3+\dfrac{(x-3\times35)}{51}$

As t is same, thus put the value of t in this equation,

$\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=1+\dfrac{(x-105)}{51}\\\dfrac{x}{36}=\dfrac{(51+x-105)}{51}\\51x=36x-54\times36\\51x-36x=1944\\x=\dfrac{1944}{15}\\x=129.6$

Thus, the value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

Learn more about the rate of speed here:

https://brainly.com/question/359790

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