SOLUTION: A train travels the distance between the station A and B in 45 minutes. if the train reduces its speed by 5km per hour it takes 48 minutes to cover this distance. what is the dist

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A train travels the distance between the station A and B in 45 minutes. if the train reduces its speed by 5km per hour it takes 48 minutes to cover this distance. what is the dist      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1044434: A train travels the distance between the station A and B in 45 minutes. if the train reduces its speed by 5km per hour it takes 48 minutes to cover this distance. what is the distance between the two stations?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Travel Rate Rule to relate rate, time, distance, RT=D
Forty-five minutes is %283%2F4%29hour and 48 minutes is %284%2F5%29hour.
                   RATE         TIME       DISTANCE

REGULAR            r            t           d

SLOWER            r-k          t+h          d


UNKNOWN VARIABLES: r,d
(unit for r is kilometers per hour)
(unit for d is kilometers)
GIVEN VARIABLE ASSIGNMENTS: system%28t=3%2F4%2Ch=4%2F5%2Ck=5%29

You would make some algebra steps to solve this system:
system%28rt=d%2C%28r-k%29%28t%2Bh%29=d%29

Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.
A train travels the distance between the station A and B in 45 minutes.
If the train reduces its speed by 5 km per hour it takes 48 minutes to cover this distance,
what is the distance between the two stations?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

45 minutes = 3%2F4 of an hour.

48 minutes = 4%2F5 of an hour.

Let "u" be the speed of the train in the first scenario. in km%2Fh.
Then the speed in the second scenario is (u-5) km%2Fh.

Then you have this equation

%284%2F5%29%2A%28u-5%29 = %283%2F4%29%2Au,

which says that the distance is the same.

Simplify it:

%284%2F5%29%2Au+-+4 = %283%2F4%29%2Au,

%284%2F5+-+3%2F4%29%2Au = 4,

%2816%2F20+-+15%2F20%29%2Au = 4,

%281%2F20%29%2Au = 4,

u = 80.

Thus the train speed is 80 km/h. 
Hence, the distance is %283%2F4%29%2A80 = 60 km.

Answer. The distance is 60 km.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A train travels the distance between the station A and B in 45 minutes. if the train reduces its speed by 5km per hour it takes 48 minutes to cover this distance. what is the distance between the two stations?
Let the distance be D

Then speed of train = matrix%281%2C5%2C+D%2F%2845%2F60%29%2C+or%2C+D%2F%283%2F4%29%2C+or%2C+4D%2F3%29

Reduced speed = matrix%281%2C5%2C+D%2F%2848%2F60%29%2C+or%2C+D%2F%284%2F5%29%2C+or%2C+5D%2F4%29

We then get the following SPEED equation: 4D%2F3+-+5+=+5D%2F4

16D - 60 = 15D ------- Multiplying by LCD, 12

16D - 15D = 60

D, or distance = highlight_green%28matrix%281%2C2%2C+60%2C+km%29%29